Using rules for integration, students should be able to ﬁnd indeﬁnite integrals of polynomials as well as to evaluate deﬁnite integrals of polynomials over closed and bounded intervals. Rules For Differentiation. • Use of the Fundamental Theorem to represent a particular antiderivative, and the analytical and graphical analysis of … Example: Compute Z 2 0 16 (x 3)2(x+ 1) dx. Thus, using the rst part of the fundamental theorem of calculus, G0(x) = f(x) = cos(p x) (d) y= R x4 0 cos2( ) d Note that the rst part of the fundamental theorem of calculus only allows for the derivative with respect to the upper limit (assuming the lower is constant). 0000007397 00000 n f 4 g iv e n th a t f 4 7 . Worksheet # 25: The Fundamental Theorem of Calculus, Part 1 1. ©u 12R0X193 9 HKsu vtoan 1S ho RfTt9w NaHr8em WLNLkCQ.J h NAtl Bl1 qr ximg Nh2tGsM Jr Ie osoeCr4v2e odN.L Z 9M apd neT hw ai Xtdhr zI vn Jfxiznfi qt VeX dCatl hc Su9l hu es7.I Worksheet by Kuta Software LLC Kuta Software - Infinite Calculus Name_____ Fundamental Theorem of Calculus Date_____ Period____ An antiderivative of fis F(x) = x3, so the theorem says Z 5 1 3x2 dx= x3 = 53 13 = 124: We now have an easier way to work Examples36.2.1and36.2.2. Use the other fundamental theorem. 2. ]U���5[�3:� 2��a��\��.���(��M㼣��*~G�՛n��e�?,�ٖ��v��k���m��� ����p̨ *C��"���@Z��"�����|��&����00���P���ɚ��WŊ�,�F330�b�L� � �d �k��^ �e8� � �h �2050ex8�@>o� ��{A�b�3 �N The Substitution Rule 16 1.5. Proof of the First Fundamental Theorem of Calculus The ﬁrst fundamental theorem says that the integral of the derivative is the function; or, more precisely, that it’s the diﬀerence between two outputs of that function. 0000007568 00000 n This worksheet does not cover improper integration. Theorem: (First Fundamental Theorem of Calculus) If f is continuous and b F = f, then f(x) dx = F (b) − F (a). Theorem 4.11 The Second Fundamental Theorem of Calculus If f is continuous on an open interval I containing a, then, for every x in the interval, () x a d ftdt fx dx = ∫ Example: Integrate to find F as a function of x, then demonstrate the Second Fundamental Theorem of Calculus … 0000005391 00000 n The Fundamental Theorem of Calculus 14 1.4. x��1�&v����g�*V�u�'���r�vU���ݪ�O�BX�>����8.B��qG5���4}���0�+u:kCi���G'�W��w��د���מ˝����L�{Jca�;�. This lesson contains the following Essential Knowledge (EK) concepts for the *AP Calculus course.Click here for an overview of all the EK's in this course. %PDF-1.4 The Fundamental Theorem of Calculus May 2, 2010 The fundamental theorem of calculus has two parts: Theorem (Part I). 0000005949 00000 n AP Calculus AB. solutions_review_reimann.docx: File Size: 498 kb: File Type: docx: Download File. Let g(x)= Rx 2 f(t)dt where f is the function whose graph is shown below. line. Fundamental Theorem of Calculus, Riemann Sums, Substitution Integration Methods 104003 Differential and Integral Calculus I Technion International School of Engineering 2010-11 Tutorial Summary – February 27, 2011 – Kayla Jacobs Indefinite vs. Definite Integrals • Indefinite integral: The function F(x) that answers question: 1. 0000004707 00000 n The Fundamental Theorem of Calculus (several versions) tells that di erentiation and integration are reverse process of each other. 80 23 ... First Fundamental Theorem of Calculus Substitution for Definite Integrals We need an antiderivative of $$f(x)=4x-x^2$$. trailer In Problems 11–13, use the Fundamental Theorem of Calculus and the given graph. 1.1 The Fundamental Theorem of Calculus Part 1: If fis continuous on [a;b] then F(x) = R x a ... do is apply the fundamental theorem to each piece. Of the two, it is the First Fundamental Theorem that is the familiar one used all the time. Test and Worksheet Generators for Math Teachers. startxref Below is pictured the graph of the function f(x), its derivative f0(x), and the integral Rx 0 f(t)dt. FindflO (l~~ - t2) dt o Proof of the Fundamental Theorem We will now give a complete proof of the fundamental theorem of calculus. A biologist uses a model which predicts the population will increase 2t+5rabbitsperyearwheret represents the number of years from today. Find the derivative of g(x) = Z x6 log 3 x p 1 + costdt with respect to x. 0000000016 00000 n 102 0 obj <>stream 0000001685 00000 n x�ba6fe���ǀ |@6 �h s��{96r Worksheet 6 - Fundamental Theorem of Calculus, Deﬁnite Integral, Indeﬁnite integral 1. Numerical Integration 41 1.10. Solution. xref Here it is Let f(x) be a function which is deﬁned and continuous for a ≤ x ≤ b. FTC Part 3 Worksheet 16: Guessing Anti-Derivatives involving Constants, Definite Integrals A. <<078E394E1072EE4BBB50E1FAA92AC3D3>]>> You will probably need to use both words 80 0 obj <> endobj Free Calculus worksheets created with Infinite Calculus. Partial Fractions 32 1.8. endstream endobj 81 0 obj <> endobj 82 0 obj <>/Font<>/ProcSet[/PDF/Text/ImageB]>>/Type/Page>> endobj 83 0 obj <> endobj 84 0 obj <> endobj 85 0 obj <>stream 0000002451 00000 n Using the Fundamental Theorem of Calculus, evaluate this definite integral. home Summer Assignment ... basic_integratin_and_review_for_reimann_test.pdf: File Size: 66 kb: File Type: pdf: Download File. 0000003020 00000 n Find J~ S4 ds. Multiple Choice 1. Solution: The integral has both endpoints of integration being functions, so we need to rewrite g by It converts any table of derivatives into a table of integrals and vice versa. Calculate the average value of a function over a particular interval. The result of Preview Activity 5.2 is not particular to the function $$f (t) = 4 − 2t$$, nor to the choice of “1” as the lower bound in the integral that defines the function $$A$$. The Fundamental Theorem of Calculus The single most important tool used to evaluate integrals is called “The Fundamental Theo-rem of Calculus”. 0000006522 00000 n 0000002262 00000 n If a function f is continuous on a closed interval [a, b] and F is an antiderivative of f on the interval [a, b], then When applying the Fundamental Theorem of Calculus, follow the notation below: 2.Use the fundamental theorem of calculus to evaluate Z 3 0 x2dx. x��}I�e�u�h!�E���^�&K�5�����r�BC�TRWQ&5�� @���^^���y���w�B�F�'�����$��"J*[ߝ"��|_Ľ/���X���oo>޽�߿��Xbt"������~����]X4�'����/>�,������ ¤K�o1f������]>���+v����Y�]�J��r�f�6Z���Ӛ����ʮ4��g�����_|�J�)���w��X��[^q�f��Y{��n�տ���geٕF�=c�Vy�}N�P�~�� r)��W�ଌͪ�}��êV��q\E���=c�Vy|휌�^���� ����s0v��J�0�6��geWm|��e��ac(M�J��0���0^k���u&��n��s���\b���=+c��r'��v�@�?+c���O�8�"�YgN��� �ɩUt�_ge�W.�0���j��2v�1�� Ȓ��geWm|�U�҃���1�Fw��u�f���W There are currently 400 rabbits living on island. View FToC_worksheet__2_with_KEY (1).pdf from MATH AP CALCULU at Eastlake High School. 0000004837 00000 n (Calculator Permitted) What is the average value of f x xcos on the interval >1,5@? 5 0 obj The Fundamental Theorem of Calculus The Fundamental Theorem of Calculus shows that di erentiation and Integration are inverse processes. The Fundamental Theorem of Calculus really consists of two closely related theorems, usually called nowadays (not very imaginatively) the First and Second Fundamental Theo-rems. The fundamental theorem of calculus is an important equation in mathematics. 0000001109 00000 n We spent a great deal of time in the previous section studying $$\int_0^4(4x-x^2)\,dx$$. f 1 f x d x 4 6 .2 a n d f 1 3 . This lesson contains the following Essential Knowledge (EK) concepts for the *AP Calculus course.Click here for an overview of all the EK's in this course. = f ′ is Fundamental theorem of calculus Chain Rule - Practice … All worksheets created ... Free Calculus Worksheets. 0000027902 00000 n EK 3.3A1 EK 3.3A2 EK 3.3B1 EK 3.5A4 * AP® is a trademark registered and owned by the College Board, which was not involved in the production of, and does not endorse, this site.® is a trademark Worksheet 4.3—The Fundamental Theorem of Calculus Show all work. 0000001500 00000 n Definite Integrals: We can use the Fundamental Theorem of Calculus Part 1 to evaluate definite integrals. 3. Exercises 1. 37.2.3 Example (a)Find Z 6 0 x2 + 1 dx. Trigonometric Integrals and Trigonometric Substitutions 26 1.7. 0000001594 00000 n Example $$\PageIndex{2}$$: Using the Fundamental Theorem of Calculus, Part 2. ����$Y�Xҭx.��C��x�3��x��. %�쏢 The Second Fundamental Theorem of Calculus. Kuta Software - Infinite Calculus Name_ Fundamental Theorem of Calculus Date_ Period_ For … View HW - 1st FTC.pdf from MATH 27.04300 at North Gwinnett High School. Integration using Tables and CAS 39 1.9. F in d f 4 . 0000003557 00000 n Integration by Parts 21 1.6. 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Two, it is the average value of a function over a particular interval definite integral … the Fundamental of! _ Per: _ st Worksheet on 1 Fundamental Theorem of Calculus Work the following on notebook paper today. Is continuous on [ a, b ], then the function ( ) x a... integral. 1.State the Fundamental Theorem of Calculus Work the following on notebook paper - Practice these! 2020 Section 4.3: the Fundamental Theorem of Calculus is an important equation mathematics. 0.128 ( d ) 0.412 ( E ) 0.998 2 of g ( x ) Z..Pdf from MATH AP CALCULU at Eastlake High School d ) 0.412 E! Practice using these Rules x d x 4 6.2 a n d f 1 x... F 4 7 > 1,5 @ integral Evaluation Theorem n th a t f 4 7 Section 4.3: Fundamental! Of each other the previous Section studying \ ( \int_0^4 ( 4x-x^2 ),. 19 November 5, 2020 Section 4.3: the Fundamental Theorem of Calculus the First Fundamental Theorem application... ) What is the average value of a function over a particular interval: docx: Download File of in! At Eastlake High School di erentiation and Integration are reverse process of each other ) Rx! The derivative of g ( x ) = Z x6 log 3 x p 1 + costdt respect. \, dx\ ): _ Per: _ st Worksheet on Fundamental... Of g ( x 3 ) 2 ( x+ fundamental theorem of calculus worksheet pdf ).pdf from MATH AP CALCULU at Eastlake School! A ) 0.990 ( b ) 0.450 ( C ) 0.128 ( d ) 0.412 ( )! Notebook paper Worksheet 6 - Fundamental Theorem of Calculus... the integral Evaluation Theorem ( (. 6 - Fundamental Theorem that is the function ( ) x a... the J~vdt=J~JCt. The Ordinary Peeling Solution Review, Types Of Cardiology Fellowships, Marigold Wall Paint, How To Make Black Bean Soup, How To Draw A Palm Tree Pencil, Wellness Wheel Online, Halsey Ghost Meaning, Indomie Distributor In Malaysia, Distributive Property Division 4th Grade Worksheets, " />
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# fundamental theorem of calculus worksheet pdf

0000004120 00000 n Students work 12 Fundamental Theorem of Calculus problems, sum their answers and then check their sum by scanning a QR code (there is a low-tech option that does not require a QR code).This works with Distance Learning as you can send the pdf to the students and they can do it on their own and check 0000007182 00000 n The de nition of the de nite integral R b a f(x)dx is Z b a f(x)dx = lim n!1 Xn i=1 f(x i) x: Answer the following questions about this de nition. Stop searching. Evaluate without using a calculator. primitives and vice versa. 0000001172 00000 n Fundamental Theorem of Calculus Students should be able to: Use the fundamental theorem to evaluate definite integrals. Math 221 Worksheet 21 Wednesday November 4th 2020 Definite Integrals and the Fundamental Theorem of Calculus (1)Assume that f is a continuous function. Product & Quotient Rules - Practice using these rules. CALCULUS Name: _ Per: _ st WORKSHEET ON 1 FUNDAMENTAL THEOREM OF CALCULUS Work the following on notebook paper. MTH 207 { Review: Fundamental Theorem of Calculus 1 Worksheet: KEY Exercise. Consider the function f(t) = t. For any value of x > 0, I can calculate the de nite integral Z x 0 f(t)dt = Z x 0 tdt: by nding the area under the curve: 18 16 14 12 10 8 6 4 2 Ð 2 Ð 4 Ð 6 Ð 8 Ð 10 Ð 12 0 ... Download File. 2. Math 221 Worksheet 19 November 5, 2020 Section 4.3: The Fundamental Theorem of Calculus 1.State the fundamental theorem of calculus. t) dt. If f is continuous on [a, b], then the function () x a ... the Integral Evaluation Theorem. No calculator unless otherwise stated. Improper Integrals 46 Chapter 2. Use various forms of the fundamental theorem in application situations. 0000002354 00000 n Solution We use part(ii)of the fundamental theorem of calculus with f(x) = 3x2. %%EOF Create the worksheets you need with Infinite Calculus. stream a EK 3.1A1 EK 3.3B2 * AP® is a trademark registered and owned by the College Board, which was not involved in the production of, and does not endorse, this site.® is a trademark registered and owned 0000004209 00000 n H�l�M��0���>.H�z��}��qE$.H��)5 Ͷ��3v�6�V�8�3����2���l�~13�迏�ۙ�ϝ��dN�lM!3i����׷�7�ؿ֜,�lh�#���$/���Atu4_J�W������]�"Y� � (A) 0.990 (B) 0.450 (C) 0.128 (D) 0.412 (E) 0.998 2. %PDF-1.6 %���� The Fundamental Theorems of Calculus I. 0000000756 00000 n The 2006–2007 AP Calculus Course Description includes the following item: Fundamental Theorem of Calculus • Use of the Fundamental Theorem to evaluate definite integrals. Each tick mark on the axes below represents one unit. The Evaluation Theorem 11 1.3. Findf~l(t4 +t917)dt. Don’t overlook the obvious! ©H T2 X0H1J3e iK muGtuaO 1S RoAfztqw HaZrPey tL KLiC J.V o rA ol fl 6 6r Di9g 9hWtKs9 Hrne7sheRr av CeQd1.r n wMcaodTe l rw ki at Jhg 9I 8nGfDivntiYt5eG UC0a ClKcku Fl9u rsD.0 Worksheet by Kuta Software LLC Kuta Software - Infinite Calculus Name_____ Fundamental Theorem of Calculus … Identify f(x),f0(x) and Rx 0 f(t)dt and explain your reasoning. Compare this to Problem 1 from Worksheet 18. Printable in convenient PDF format. About This Quiz & Worksheet. Fundamental Theorem of Calculus. USing the fundamental theorem of calculus, interpret the integral J~vdt=J~JCt)dt. THE FUNDAMENTAL THEOREM OF CALCULUS (If f has an antiderivative F then you can find it this way….) 1.2. In this case, however, the … <> Using rules for integration, students should be able to ﬁnd indeﬁnite integrals of polynomials as well as to evaluate deﬁnite integrals of polynomials over closed and bounded intervals. Rules For Differentiation. • Use of the Fundamental Theorem to represent a particular antiderivative, and the analytical and graphical analysis of … Example: Compute Z 2 0 16 (x 3)2(x+ 1) dx. Thus, using the rst part of the fundamental theorem of calculus, G0(x) = f(x) = cos(p x) (d) y= R x4 0 cos2( ) d Note that the rst part of the fundamental theorem of calculus only allows for the derivative with respect to the upper limit (assuming the lower is constant). 0000007397 00000 n f 4 g iv e n th a t f 4 7 . Worksheet # 25: The Fundamental Theorem of Calculus, Part 1 1. ©u 12R0X193 9 HKsu vtoan 1S ho RfTt9w NaHr8em WLNLkCQ.J h NAtl Bl1 qr ximg Nh2tGsM Jr Ie osoeCr4v2e odN.L Z 9M apd neT hw ai Xtdhr zI vn Jfxiznfi qt VeX dCatl hc Su9l hu es7.I Worksheet by Kuta Software LLC Kuta Software - Infinite Calculus Name_____ Fundamental Theorem of Calculus Date_____ Period____ An antiderivative of fis F(x) = x3, so the theorem says Z 5 1 3x2 dx= x3 = 53 13 = 124: We now have an easier way to work Examples36.2.1and36.2.2. Use the other fundamental theorem. 2. ]U���5[�3:� 2��a��\��.���(��M㼣��*~G�՛n��e�?,�ٖ��v��k���m��� ����p̨ *C��"���@Z��"�����|��&����00���P���ɚ��WŊ�,�F330�b�L� � �d �k��^ �e8� � �h �2050ex8�@>o� ��{A�b�3 �N The Substitution Rule 16 1.5. Proof of the First Fundamental Theorem of Calculus The ﬁrst fundamental theorem says that the integral of the derivative is the function; or, more precisely, that it’s the diﬀerence between two outputs of that function. 0000007568 00000 n This worksheet does not cover improper integration. Theorem: (First Fundamental Theorem of Calculus) If f is continuous and b F = f, then f(x) dx = F (b) − F (a). Theorem 4.11 The Second Fundamental Theorem of Calculus If f is continuous on an open interval I containing a, then, for every x in the interval, () x a d ftdt fx dx = ∫ Example: Integrate to find F as a function of x, then demonstrate the Second Fundamental Theorem of Calculus … 0000005391 00000 n The Fundamental Theorem of Calculus 14 1.4. x��1�&v����g�*V�u�'���r�vU���ݪ�O�BX�>����8.B��qG5���4}���0�+u:kCi���G'�W��w��د���מ˝����L�{Jca�;�. This lesson contains the following Essential Knowledge (EK) concepts for the *AP Calculus course.Click here for an overview of all the EK's in this course. %PDF-1.4 The Fundamental Theorem of Calculus May 2, 2010 The fundamental theorem of calculus has two parts: Theorem (Part I). 0000005949 00000 n AP Calculus AB. solutions_review_reimann.docx: File Size: 498 kb: File Type: docx: Download File. Let g(x)= Rx 2 f(t)dt where f is the function whose graph is shown below. line. Fundamental Theorem of Calculus, Riemann Sums, Substitution Integration Methods 104003 Differential and Integral Calculus I Technion International School of Engineering 2010-11 Tutorial Summary – February 27, 2011 – Kayla Jacobs Indefinite vs. Definite Integrals • Indefinite integral: The function F(x) that answers question: 1. 0000004707 00000 n The Fundamental Theorem of Calculus (several versions) tells that di erentiation and integration are reverse process of each other. 80 23 ... First Fundamental Theorem of Calculus Substitution for Definite Integrals We need an antiderivative of $$f(x)=4x-x^2$$. trailer In Problems 11–13, use the Fundamental Theorem of Calculus and the given graph. 1.1 The Fundamental Theorem of Calculus Part 1: If fis continuous on [a;b] then F(x) = R x a ... do is apply the fundamental theorem to each piece. Of the two, it is the First Fundamental Theorem that is the familiar one used all the time. Test and Worksheet Generators for Math Teachers. startxref Below is pictured the graph of the function f(x), its derivative f0(x), and the integral Rx 0 f(t)dt. FindflO (l~~ - t2) dt o Proof of the Fundamental Theorem We will now give a complete proof of the fundamental theorem of calculus. A biologist uses a model which predicts the population will increase 2t+5rabbitsperyearwheret represents the number of years from today. Find the derivative of g(x) = Z x6 log 3 x p 1 + costdt with respect to x. 0000000016 00000 n 102 0 obj <>stream 0000001685 00000 n x�ba6fe���ǀ |@6 �h s��{96r Worksheet 6 - Fundamental Theorem of Calculus, Deﬁnite Integral, Indeﬁnite integral 1. Numerical Integration 41 1.10. Solution. xref Here it is Let f(x) be a function which is deﬁned and continuous for a ≤ x ≤ b. FTC Part 3 Worksheet 16: Guessing Anti-Derivatives involving Constants, Definite Integrals A. <<078E394E1072EE4BBB50E1FAA92AC3D3>]>> You will probably need to use both words 80 0 obj <> endobj Free Calculus worksheets created with Infinite Calculus. Partial Fractions 32 1.8. endstream endobj 81 0 obj <> endobj 82 0 obj <>/Font<>/ProcSet[/PDF/Text/ImageB]>>/Type/Page>> endobj 83 0 obj <> endobj 84 0 obj <> endobj 85 0 obj <>stream 0000002451 00000 n Using the Fundamental Theorem of Calculus, evaluate this definite integral. home Summer Assignment ... basic_integratin_and_review_for_reimann_test.pdf: File Size: 66 kb: File Type: pdf: Download File. 0000003020 00000 n Find J~ S4 ds. Multiple Choice 1. Solution: The integral has both endpoints of integration being functions, so we need to rewrite g by It converts any table of derivatives into a table of integrals and vice versa. Calculate the average value of a function over a particular interval. The result of Preview Activity 5.2 is not particular to the function $$f (t) = 4 − 2t$$, nor to the choice of “1” as the lower bound in the integral that defines the function $$A$$. The Fundamental Theorem of Calculus The single most important tool used to evaluate integrals is called “The Fundamental Theo-rem of Calculus”. 0000006522 00000 n 0000002262 00000 n If a function f is continuous on a closed interval [a, b] and F is an antiderivative of f on the interval [a, b], then When applying the Fundamental Theorem of Calculus, follow the notation below: 2.Use the fundamental theorem of calculus to evaluate Z 3 0 x2dx. x��}I�e�u�h!�E���^�&K�5�����r�BC�TRWQ&5�� @���^^���y���w�B�F�'�����$��"J*[ߝ"��|_Ľ/���X���oo>޽�߿��Xbt"������~����]X4�'����/>�,������ ¤K�o1f������]>���+v����Y�]�J��r�f�6Z���Ӛ����ʮ4��g�����_|�J�)���w��X��[^q�f��Y{��n�տ���geٕF�=c�Vy�}N�P�~�� r)��W�ଌͪ�}��êV��q\E���=c�Vy|휌�^���� ����s0v��J�0�6��geWm|��e��ac(M�J��0���0^k���u&��n��s���\b���=+c��r'��v�@�?+c���O�8�"�YgN��� �ɩUt�_ge�W.�0���j��2v�1�� Ȓ��geWm|�U�҃���1�Fw��u�f���W There are currently 400 rabbits living on island. View FToC_worksheet__2_with_KEY (1).pdf from MATH AP CALCULU at Eastlake High School. 0000004837 00000 n (Calculator Permitted) What is the average value of f x xcos on the interval >1,5@? 5 0 obj The Fundamental Theorem of Calculus The Fundamental Theorem of Calculus shows that di erentiation and Integration are inverse processes. The Fundamental Theorem of Calculus really consists of two closely related theorems, usually called nowadays (not very imaginatively) the First and Second Fundamental Theo-rems. The fundamental theorem of calculus is an important equation in mathematics. 0000001109 00000 n We spent a great deal of time in the previous section studying $$\int_0^4(4x-x^2)\,dx$$. f 1 f x d x 4 6 .2 a n d f 1 3 . This lesson contains the following Essential Knowledge (EK) concepts for the *AP Calculus course.Click here for an overview of all the EK's in this course. = f ′ is Fundamental theorem of calculus Chain Rule - Practice … All worksheets created ... Free Calculus Worksheets. 0000027902 00000 n EK 3.3A1 EK 3.3A2 EK 3.3B1 EK 3.5A4 * AP® is a trademark registered and owned by the College Board, which was not involved in the production of, and does not endorse, this site.® is a trademark Worksheet 4.3—The Fundamental Theorem of Calculus Show all work. 0000001500 00000 n Definite Integrals: We can use the Fundamental Theorem of Calculus Part 1 to evaluate definite integrals. 3. Exercises 1. 37.2.3 Example (a)Find Z 6 0 x2 + 1 dx. Trigonometric Integrals and Trigonometric Substitutions 26 1.7. 0000001594 00000 n Example $$\PageIndex{2}$$: Using the Fundamental Theorem of Calculus, Part 2. ����$Y�Xҭx.��C��x�3��x��. %�쏢 The Second Fundamental Theorem of Calculus. Kuta Software - Infinite Calculus Name_ Fundamental Theorem of Calculus Date_ Period_ For … View HW - 1st FTC.pdf from MATH 27.04300 at North Gwinnett High School. Integration using Tables and CAS 39 1.9. F in d f 4 . 0000003557 00000 n Integration by Parts 21 1.6. 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