### Home > APCALC > Chapter 5 > Lesson 5.2.5 > Problem5-107

5-107.

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

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

You could rewrite the integrand as a piecewise function. Or you could sketch the graph (it's a transformation of $y = \left|x\right|$) and use geometry.

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

Before you integrate, rewrite the integrand with exponents.

3. $\int _ { 5 } ^ { 5 } \operatorname { log } ( \sqrt { 2 u ^ { 5 } + 1 } ) d u$

Notice the bounds.

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

Don't panic! What famous trig function has a derivative of $\sec^2x$?

$\tan x+C$