### Home > CALC > Chapter 4 > Lesson 4.3.1 > Problem4-98

4-98.

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. $\int _ { - \pi } ^ { \pi } \operatorname { cos } x d x$

To make this problem quicker to solve, remember that
$y =\operatorname{cos}x$ is an even function.

$=2\int_{0}^{\pi}\text{cos}xdx=2\left ( \text{sin}x\left|\begin{matrix} \pi \\ 0 \end{matrix}\right. \right )=2[\text{sin}\pi -\text{sin}0]=0$

1. $\int ( 5 \sqrt { y } - \operatorname { sin } y ) d y$

Notice that this is an indefinite integral. Don't forget the $+C$.

1. $\int _ { 1 } ^ { 2.7183 } \frac { 1 } { x } d x$

$2.7183 ≈ e$ (Euler's number) and the derivative of ln$(x)$ is $x^{−1}$.

1. $\int ( \operatorname { sin } ^ { 2 } x + \operatorname { cos } ^ { 2 } x ) d x$

Think! Trig identity. Simplify the integrand before you integrate.