### Home > APCALC > Chapter 6 > Lesson 6.1.1 > Problem6-12

6-12.

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

1. $\int _ { 0 } ^ { \pi / 3 } \operatorname { sec } ^ { 2 } ( x ) d x$

$\text{Recall that }\frac{d}{dx}\text{tan}(x)=\text{sec}^{2}(x)$

1. $\int ( \operatorname { sec } ( y ) \operatorname { tan } ( y ) - 5 y ^ { 3 / 2 } ) d y$

$\text{Recall that }\frac{d}{dx}\text{sec}(y)=\text{tan}(y)\text{sec}(y)$

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

$≈ 0.328$
(By calculator, unless you know the antiderivative
of $y = \arcsin(x)$.)

1. $\int ( t ^ { 2 } - 3 ) ^ { 2 } d t$

Before you integrate, expand the integrand.