### Home > APCALC > Chapter 5 > Lesson 5.2.4 > Problem5-96

5-96.

Evaluate the following integral expressions without a calculator.

1. $\int _ { 1 } ^ { 8 } ( \sqrt [ 3 ] { 27 u } ) d u$

Before integrating, rewrite the integrand with a fractional exponent. Note that both the $27$ and the $u$ are beneath the radical sign!

2. $\frac { d } { d x } ( \int _ { 4 } ^ { 18 } ( 6 x - 3 ) d x )$

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.

$0$
Explain.

3. $\int f ^ { \prime \prime } ( x ) d x$

$=\int \frac{d}{dx}f'(x)dx=\underline{ \ \ \ \ \ \ \ \ \ \ \ \ } +C$

Think: Fundamental Theorem of Calculus, part 1.