CPM Homework Help : APCALC Problem 9-109

Examine the integrals below. Consider the multiple tools available for integrating and use the best strategy for each part. Evaluate each integral and briefly describe your method.

$\int _ { 0 } ^ { \pi } \frac { \operatorname { sin } ( x ) } { 2 - \operatorname { cos } ( x ) } d x$
Hint (a):
Use substitution. Let $u = -\cos(x)$ .

$\int _ { - 6 } ^ { 2 } | x | d x$
Hint (b):
This integral can be evaluated by sketching the graph and using geometry.

$\int x ^ { 2 } e ^ { 4 x } d x$
Hint (c):
Use integration by parts.
Step (c):
Let $f = x^2$ and $dg = e^{4x}$ .

$\int _ { 0 } ^ { \infty } \frac { x } { x ^ { 2 } + 4 } d x$
Hint (d):
Use substitution. Let $u = x^2 + 4$ .