### Home > APCALC > Chapter 5 > Lesson 5.3.1 > Problem5-117

5-117.

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

1. $\int _ { - 2 } ^ { 1 } ( 3 x + 1 ) ^ { 2 } d x$

Before integrating, expand the integrand.

2. $\int \operatorname { csc } ^ { 2 } ( x ) d x$

Think about the derivatives of common trig functions. Be mindful about the sign of your antiderivative.

3. $\int _ { x } ^ { 0 } \operatorname { sin } ( t ) d t$

Refer to hint in part (b).

4. $\int _ { 0 } ^ { \pi } \operatorname { cot } ( x ) \operatorname { tan } ( x ) d x$

Refer to hint in part (b).