I'm working on a tricky problem. Hopefully I got it right.
If is approximated by three inscribed rectangles of equal width on the x-axis. Determine the approximation of this integral.
After I graphed it, I found that the minimum is actually at 1. So the height of the first and second rectangles is 2. Therefore, their total area: .
The third rectangle's height: .
Total area: .
Did I do it correctly? Hopefully I got this one right. Thanks everyone.
The integrand is a parabola opening upwards. It has a minimum of at .
The three rectangle have equal widths so they extend from to , to and to .
So the first inscribed rectangle has height , the second has height and the third height , where .
This is much easier to see if you draw a diagram.