CPM Homework Help : APCALC Problem 7-206

CPM Homework Banner

Home > APCALC > Chapter 7 > Lesson 7.4.3 > Problem 7-206

7-206.

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.

$\int _ { - 1 } ^ { 3 } \frac { d x } { x }$
Hint (a):
This is an improper integral because $y=\frac{1}{x}$ has a vertical asymptote at $x=0$ .
Rewrite properly (with limits) before evaluating.

$\int \operatorname { tan } ^ { - 1 } ( x ) d x$
Hint (b):
Use integration by parts after you rewrite the integrand as $\arctan(x)$ .
Let $f(x) = \arctan(x)$ and $dg = dx$ .
Then $df = \text{_______}$ and $g(x) = \text{_______}$ .
Warning: You will have to use $U$ -substitution to evaluate the integral.

$\int \frac { \operatorname { sin } \sqrt { x } d x } { \sqrt { x } }$
Hint (c):
$\text{Use }U\text{-Substitution}. \text{ Let }U=\sqrt{x}.$

$\int _ { \pi / 3 } ^ { \pi / 2 } \operatorname { csc } ^ { 2 } ( x ) d x$
Hint (d):
$\text{Recall that }\frac{d}{dx}\cot(x)=-\csc^2(x).$

© 2022 CPM Educational Program. All rights reserved.