### Home > APCALC > Chapter 8 > Lesson 8.1.6 > Problem8-59

8-59.

No calculator! Integrate. Homework Help ✎

1. $\int _ { 0 } ^ { 8 } | x - 4 | d x$

You could rewrite the integrand as a piecewise function and then integrate each piece separately, or...

You could think about the shape of the graph of $y = |x − 4|$and evaluate this integral geometrically.

1. $\int w ( w ^ { 2 } - 1 ) d w$

Before integrating, distribute the $w$.

1. $\int _ { - 1 } ^ { - 5 } - 7 d x$

Before integrating, think about the shape of the graph of $y = −7$. Evaluate this integral geometrically. Careful: Will the area be positive or negative?

1. $\int _ { 0 } ^ { 5 } \sqrt { 25 - x ^ { 2 } } d x$

$\text{Before integrating, think about the shape of the graph of }y=\sqrt{25-x^{2}}.$

Evaluate this integral geometrically.