### Home > APCALC > Chapter 9 > Lesson 9.4.1 > Problem9-109

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.

1. $\int _ { 0 } ^ { \pi } \frac { \operatorname { sin } ( x ) } { 2 - \operatorname { cos } ( x ) } d x$

Use substitution. Let $u = -\cos(x)$.

1. $\int _ { - 6 } ^ { 2 } | x | d x$

This integral can be evaluated by sketching the graph and using geometry.

1. $\int x ^ { 2 } e ^ { 4 x } d x$

Use integration by parts.

Let $f = x^2$ and $dg = e^{4x}$.

1. $\int _ { 0 } ^ { \infty } \frac { x } { x ^ { 2 } + 4 } d x$

Use substitution. Let $u = x^2 + 4$.