Area between curves, with an absolute value function

[tangibleLime]

Homework Statement

Then find the area S of the region. (between the curves)

Homework Equations

$$A = \int_a^b f(x)-g(x) dx$$

The Attempt at a Solution

First I plotted both equations, determined the top and the bottom functions and found where they intersected (calculator).

Then I set up the problem according the the area formula above...
$$A = \int_{-10}^{10} ((|9x|)-(x^2-10))dx$$

Then I found the antiderivatives for each function...
$$(\frac{9x}{\sqrt{x^2}})-(\frac{x^3}{3}-10x)$$

Then I subtracted the two bounds...
$$((\frac{9(10)}{\sqrt{(10)^2}})-(\frac{(10)^3}{3}-10(10))) - ((\frac{9(-10)}{\sqrt{(-10)^2}})-(\frac{(-10)^3}{3}-10(-10)))$$

This gave me the final answer of $$\frac{-1346}{3}$$, which was wrong. I assume my problem is the absolute value sign... because this method works fine with other problems of the same nature that don't have an absolute value as one of the functions.

Any help would be appreciated.

 

[Inferior89]

|x| is x when x > 0 and -x when x < 0.

Split up the case when x > 0 and x < 0 and add up the areas for both cases.