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MATH 12 Worksheet 2: Fundamental Theorem of Calculus 1. Definite Integrals and the Fundamental Theorem of Calculus (a) Sketch the boundary and shade the region of integration indicated by the integral. Com- pute the area using geometry, not the FTC. i. f 5 dx ii. ³₂(2x + 4) dx iii. f √25 - x² dx iv. ²₁(5 - x + x) dx i. f¹0 5x² dx ii. f(x+4) dx iii. ² sin(x) dx iv. 5/6 (sec²(x)) dx (b) Evaluate each of the following integrals using the FTC. Look carefully at the intervals and functions to decide an appropriate approach before you start. A S4/9 6³/2-4¹/2 dx vi. f(x5 + 3x³ - 10x) dx vii. (25 + 3x³ - 10x) dx V. (c) Concept Check: Suppose that f(x) is an even function with fo f(x) dx = 11. Find f³3 f(x) dx. (x) dx = 11. Find

MATH 12 Worksheet 2: Fundamental Theorem of Calculus 1. Definite Integrals and the Fundamental Theorem of Calculus (a) Sketch the boundary and shade the region of integration indicated by the integral. Com- pute the area using geometry, not the FTC. i. f 5 dx ii. ³₂(2x + 4) dx iii. f √25 - x² dx iv. ²₁(5 - x + x) dx i. f¹0 5x² dx ii. f(x+4) dx iii. ² sin(x) dx iv. 5/6 (sec²(x)) dx (b) Evaluate each of the following integrals using the FTC. Look carefully at the intervals and functions to decide an appropriate approach before you start. A S4/9 6³/2-4¹/2 dx vi. f(x5 + 3x³ - 10x) dx vii. (25 + 3x³ - 10x) dx V. (c) Concept Check: Suppose that f(x) is an even function with fo f(x) dx = 11. Find f³3 f(x) dx. (x) dx = 11. Find

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 67E
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Solve vii, from section b. Evaluate the integral using the FTC(fundamentals theorem of calculus). Look carefully at the intervals and functions to decide an appropriate approach. 

MATH 12 Worksheet 2: Fundamental Theorem of Calculus 1. Definite Integrals and the Fundamental Theorem of Calculus (a) Sketch the boundary and shade the region of integration indicated by the integral. Com- pute the area using geometry, not the FTC. i. So 5 dx ii. ³₂ (2x + 4) dx -2 10 2 i. f¹0 5x² dx (b) Evaluate each of the following integrals using the FTC. Look carefully at the intervals and functions to decide an appropriate approach before you start. 1 ii. _3²¹ (x+4) dx -3 iii. f/2 sin(x) dx √25 - x² dx iii. iv. 2₁ (5-x+x) dx π/6 iv. f/6 (sec²(x)) dx dx vi. (x5 + 3x³ - 10x)dx 4 vii. f(x5 + 3x³ - 10x) dx V. A 6x3/2-4x¹/2 3 (c) Concept Check: Suppose that f(x) is an even function with fo f(x) dx = 11. Find f³3 f(x) dx. 3 f(x) dx = 11. Find Chodlr. Suppor that f(r) is an odd function with f f(x) dx
Transcribed Image Text:MATH 12 Worksheet 2: Fundamental Theorem of Calculus 1. Definite Integrals and the Fundamental Theorem of Calculus (a) Sketch the boundary and shade the region of integration indicated by the integral. Com- pute the area using geometry, not the FTC. i. So 5 dx ii. ³₂ (2x + 4) dx -2 10 2 i. f¹0 5x² dx (b) Evaluate each of the following integrals using the FTC. Look carefully at the intervals and functions to decide an appropriate approach before you start. 1 ii. _3²¹ (x+4) dx -3 iii. f/2 sin(x) dx √25 - x² dx iii. iv. 2₁ (5-x+x) dx π/6 iv. f/6 (sec²(x)) dx dx vi. (x5 + 3x³ - 10x)dx 4 vii. f(x5 + 3x³ - 10x) dx V. A 6x3/2-4x¹/2 3 (c) Concept Check: Suppose that f(x) is an even function with fo f(x) dx = 11. Find f³3 f(x) dx. 3 f(x) dx = 11. Find Chodlr. Suppor that f(r) is an odd function with f f(x) dx
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