### Home > CALC > Chapter 6 > Lesson 6.2.1 > Problem6-61

6-61.

Examine the integrals below. Consider the multiple tools available for evaluating integrals and use the best strategy for each. After evaluating the integral, write a short description of your method.

1. $\int _ { \pi / 6 } ^ { \pi / 4 } ( \operatorname { csc } ^ { 2 }( x )) d x$

Think! What function has a derivative of $y=\operatorname{csc}^2x$? Be mindful about positive and negative signs.

1. $\int ( 5 ^ { y } - 3 ( 2 y + 1 ) ^ { 2 } \cdot 2 ) d y$

Before you integrate, expand the integrand.

1. $\int _ { 0 } ^ { \pi / 4 } \operatorname { tan }( t )d t$

Use your calculator. (Unless you know what the antiderivative of $y =\operatorname{tan}x$ is).

1. $\int ( \operatorname { tan } ^ { 2 } (y) + 1 ) d y$

Continue to simplify the integrand, and then evaluate.