CPM Homework Help : CALC Problem 5-107

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5-107.

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.

$\int _ { - 3 } ^ { 2 } ( - | x + 1 | + 2 ) d x$
Hint (a):
You could rewrite the integrand as a piecewise function. Or you could sketch the graph (it's a transformation of $y = |x|$ ) and use geometry.

$\int ( \frac { 2 } { t ^ { 2 } } - t ^ { 3 } ) d t$
Hint (b):
Before you integrate, rewrite the integrand with exponents.

$\int _ { 5 } ^ { 5 } \operatorname { log } ( \sqrt { 2 u ^ { 5 } + 1 } ) d u$
Hint (c):
Notice the bounds.

$\int \operatorname { sec } ^ { 2 } ( x ) d x$
Hint (d):
Don't panic! What famous trig function has a derivative of $\operatorname{sec}^2x$ ?
Answer (d):
$\operatorname{tan}x + c$

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