CPM Homework Help : CALC Problem 4-150

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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.

Hint:

$\int _ { - 1 } ^ { 1 } \sqrt { x ^ { 2 } } d x$
Hint 1(a):
$\sqrt{x^{2}}=\left | x \right |$
Hint 2(a):
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 $x = 1$ ?

$\int ( 8 x ^ { 3 } - \frac { 1 } { 2 } x ) d x$
Hint (b):
This is an indefinite integral. Don't forget the $+C$ .

$\int _ { 1 } ^ { 5 } \frac { 3 x ^ { 2 } - 5 x - 2 } { 3 x + 1 } d x$
Hint (c):
Before you integrate, factor the numerator and simplify.

$\int [ \frac { d } { d x } ( y ) ] d x$
Hint (d):
Integrating a derivative gives you the original function $+C$ .
Answer (d):
$yr + C$

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