Finding the average value of a(x) on an interval.
I'm given a problem with a diagram. Here is my bad recreation of it (there's really a point of inflection at the upper corners of the rectangle ...). The curve is y=e^-2x^2 (this means that it's x squared and then x squared is multiplied by -2) and the vertices of this rectangle inscribed under the curve are (x, 0) and (-x, 0).
This question had 2 other parts that I was able to solve correctly.
-Find A(1) with A(x) being the area of the rectangle inscribed under this curve y=e^-2x^2
A(1) is 2/e^2
Then the next question was the max value of a(x) which was e^-0.5 (I got this by taking the derivative).
Then I'm told to find the average value of a(x) in the interval 0 =< x =< 2.
Does this mean that I have to include the stuff (the part of the rectangle above in the diagram that's to the left of the y axis) that's from 0 to -x in the average area, or do I ignore that?