1. Evaluate each of the following integrals using the indicated technique. (Additional tech- niques may also be required.) dx, trigonometric integration strategies (a) [ 2x²-4x-1 dx, partial fractions 3x3x2+3x+1 cos (3x) (b) sin(3x) (c) S 2√2 (d) x²-25 23 I da, trigonometric substitution √16-x² da, trigonometric substitution 2. Evaluate the improper integral or show that it is divergent. L² x²e4 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 34E
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1. Evaluate each of the following integrals using the indicated technique. (Additional tech-
niques may also be required.)
dx, trigonometric integration strategies
(a) [
2x²-4x-1
dx, partial fractions
3x3x2+3x+1
cos (3x)
(b)
sin(3x)
(c)
S
2√2
(d)
x²-25
23
I
da, trigonometric substitution
√16-x²
da, trigonometric substitution
2. Evaluate the improper integral
or show that it is divergent.
L²
x²e4 dx
Transcribed Image Text:1. Evaluate each of the following integrals using the indicated technique. (Additional tech- niques may also be required.) dx, trigonometric integration strategies (a) [ 2x²-4x-1 dx, partial fractions 3x3x2+3x+1 cos (3x) (b) sin(3x) (c) S 2√2 (d) x²-25 23 I da, trigonometric substitution √16-x² da, trigonometric substitution 2. Evaluate the improper integral or show that it is divergent. L² x²e4 dx
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