iv. f/6(sec²(x)) dx

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter8: Further Techniques And Applications Of Integration
Section8.2: Integration By Parts
Problem 36E
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Question

Evaluate b) iv. 

(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
(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.
-10
i. ¹0 5x² dx
ii. S−3² (x+4) dx
-3
iii. 5/² sin(x) dx
iii. f √25 - x² dx
iv. 2₁ (5-x+x) dx
iv. 5/6 (sec²(x)) dx
π/6
dx
√4/962³/2-47¹/2
vi. f(x5 + 3x³ - 10x) dx
vii. f(x5 + 3x³ - 10x)dx
V.
(c) Concept Check: Suppose that f(x) is an even function with fo f(x) dx = 11. Find
√³3
-3 f(x) dx.
(d) Concept Check: Suppose that f(x) is an odd function with fo f(x) dx = 11. Find
f³3 f(x) dx.
Transcribed Image Text:(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 (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. -10 i. ¹0 5x² dx ii. S−3² (x+4) dx -3 iii. 5/² sin(x) dx iii. f √25 - x² dx iv. 2₁ (5-x+x) dx iv. 5/6 (sec²(x)) dx π/6 dx √4/962³/2-47¹/2 vi. f(x5 + 3x³ - 10x) dx vii. f(x5 + 3x³ - 10x)dx V. (c) Concept Check: Suppose that f(x) is an even function with fo f(x) dx = 11. Find √³3 -3 f(x) dx. (d) Concept Check: Suppose that f(x) is an odd function with fo f(x) dx = 11. Find f³3 f(x) dx.
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