CPM Homework Help : CALC Problem 5-18

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Home > CALC > Chapter Ch5 > Lesson 5.1.2 > Problem 5-18

5-18.

Simplify each expression.

Hint:

$\int \frac { ( m ^ { 3 } - 1 ) ^ { 2 } } { m ^ { 5 } } d m$
Steps (a):
1. Simplify the integrand by expanding the numerator and cancelling out the denominator.
2. Integrate by 'undoing' the Power Rule.
3. Don't forget the $+C$ .

$\int _ { 0 } ^ { 5 } ( \frac { d } { d x } \sqrt { x ^ { 2 } + 11 } ) d x$
Hint (b):
Fundamental Theorem of Calculus (an extension):The integral of a derivative will give us the original function $+C$ .
Answer (b):
$6-\sqrt{11}$

$\frac { d } { d x } [ \int _ { 0 } ^ { 5 } ( \frac { d } { d x } \sqrt { x ^ { 2 } + 11 } ) d x ]$
Hint (c):
$=\frac{d}{dx}[\text{part (b)}]$

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