CPM Homework Help : CALC Problem 5-96

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5-96.

Simplify the following without a calculator.

$\int _ { 1 } ^ { 8 } ( \sqrt [ 3 ] { 27 u } ) d u$
Hint (a):
Before integrating, rewrite the integrand with a fractional exponent. Note that both the $27$ and the $u$ are beneath the radical sign!

$\frac { d } { d x } ( \int _ { 4 } ^ { 18 } ( 6 x - 3 ) d x )$
Hint (b):
The Fundamental Theorem of Calculus, part 1 states that the derivative of an indefinite integral gives you the original function. But this is the derivative of a DEFINITE integral.
Answer (b):
$0$
Explain.

$\int f ^ { \prime \prime } ( x ) d x$
Hint (c):
$=\int \frac{d}{dx}f'(x)dx=\underline{ \ \ \ \ \ \ \ \ \ \ \ \ } +C$
Think: Fundamental Theorem of Calculus, part $1$ .

Compute without a calculator

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