How do I correctly find the area bounded by x=-3, y=-x^2-2x, and y=x^2-4?

[Danny222444]

Homework Statement

FInd the area bounded by x=-3, y=-x^2-2x, and y=x^2-4. (Hint: Graph the picture)

2. The attempt at a solution
My professor did set up the problem in class, but its throwing me off. He set it up as the lower bound -3 to 2, with the function (2x^2+2x-4)dx. I tried solving this but I keep getting a negative number. Any idea on what I am doing wrong?

 

[DrClaude]

Please give some details of your attempt at a solution.

 

[Danny222444]

Ok, I end up with Area=2(-2^3/3)-2^2-4(-2)-(2(-3^3/3)+(-3)^2-4(-3) and I end with -5/3. I know the area cannot be negative. I have a feeling the upper bound is wrong or -x^2-2x should be the top curve. But my professor set it up exactly like this, and I just can't seem to solve it.

 

[DrClaude]

Ok, I end up with Area=2(-2^3/3)-2^2-4(-2)-(2(-3^3/3)+(-3)^2-4(-3) and I end with -5/3. I know the area cannot be negative. I have a feeling the upper bound is wrong or -x^2-2x should be the top curve. But my professor set it up exactly like this, and I just can't seem to solve it.

First, be careful when you write the equation: I guess you mean (-2)^3, not -2^3, etc.

Second, there is a problem with the signs in that equation for the area. How are you treating the part of the area that is below y = 0?