CPM Homework Help : CALC Problem 6-12

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.

$\int _ { 0 } ^ { \pi / 3 } \operatorname { sec } ^ { 2 } x d x$
Hint (a):
Recall that $\frac{d}{dx}\text{tan}(x)=\text{sec}^{2}(x)$

$\int ( \operatorname { sec } y \operatorname { tan } y - 5 y ^ { 3 / 2 } ) d y$
Hint (b):
Recall that $\frac{d}{dx}\text{sec}(y)=\text{tan}(y)\text{sec}(y)$

$\int _ { 0 } ^ { \pi / 4 } \operatorname { arcsin } x d x$
Answer (c):
$≈ 0.328$ (By calculator, unless you know the antiderivative
of $y=\arcsin(x)$ .

$\int ( t ^ { 2 } - 3 ) ^ { 2 } d t$
Hint (d):
Before you integrate, expand the integrand.