Evaluate the integral below by interpreting it in terms of areas. In other words, draw a picture of the region the integral represents, and find the area using high school geometry. I don't know why, but I'm messing this up. I do x = 3 (so y = 0) and x = -3 (so $\displaystyle y = 3 \sqrt 2$) to get a graph that looks like a triangle. Using simply geometry to find the answer, I do 6 (the base) * $\displaystyle 3 \sqrt 2$ (the height) divided by 2 to get $\displaystyle 9 \sqrt 2$. Which is wrong.

But why?