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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.

$\int _ { - \pi } ^ { \pi } \operatorname { cos } x d x$
Hint (a):
To make this problem quicker to solve, remember that
$y =\operatorname{cos}x$ is an even function.
Answer (a):
$=2\int_{0}^{\pi}\text{cos}xdx=2\left ( \text{sin}x\left|\begin{matrix} \pi \\ 0 \end{matrix}\right. \right )=2[\text{sin}\pi -\text{sin}0]=0$

$\int ( 5 \sqrt { y } - \operatorname { sin } y ) d y$
Hint (b):
Notice that this is an indefinite integral. Don't forget the $+C$ .

$\int _ { 1 } ^ { 2.7183 } \frac { 1 } { x } d x$
Hint (c):
$2.7183 ≈ e$ (Euler's number) and the derivative of ln $(x)$ is $x^{−1}$ .

$\int ( \operatorname { sin } ^ { 2 } x + \operatorname { cos } ^ { 2 } x ) d x$
Hint (d):
Think! Trig identity. Simplify the integrand before you integrate.

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