CPM Homework Help : CALC Problem 5-32

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5-32.

Examine the integrals below. 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.

$\int _ { 1 } ^ { 4 } ( 2 x + 1 ) ^ { 2 } d x$
Hint (a):
Expand the integrand first.

$\int _ { - \pi } ^ { \pi } x \operatorname { cos } x d x$
Hint 1(b):
Can you calculate the integral just by looking at the graph?
Hint 2(b):
Without graphing, how could you have recognized that the integrand is odd?

$\int ( 2 \operatorname { sin } ^ { 2 } x + 2 \operatorname { cos } ^ { 2 } x ) d x$
Hint (c):
Factor and use a trigonometry identity.
Answer (c):
$\int 2(\text{sin}^{2}x+\text{cos}^{2}x)dx=\int 2dx= 2x+C$

$\int ( \frac { t ^ { 2 } } { 2 } - \frac { 2 } { t ^ { 2 } } ) d t$
Hint (d):
How could you simplify so you can use the Power Rule?

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