### Home > CALC > Chapter 4 > Lesson 4.4.3 > Problem4-150

4-150.

Examine the following integrals. 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. $\int _ { - 1 } ^ { 1 } \sqrt { x ^ { 2 } } d x$

$\sqrt{x^{2}}=\left | x \right |$

Simplify the integrand and then visualize the graph.
What type of symmetry does it have? What can you conclude about its area between $x = −1$ and $x = 1$?

1. $\int ( 8 x ^ { 3 } - \frac { 1 } { 2 } x ) d x$

This is an indefinite integral. Don't forget the $+C$.

1. $\int _ { 1 } ^ { 5 } \frac { 3 x ^ { 2 } - 5 x - 2 } { 3 x + 1 } d x$

Before you integrate, factor the numerator and simplify.

1. $\int [ \frac { d } { d x } ( y ) ] d x$

Integrating a derivative gives you the original function $+C$.

$yr + C$