Thread: approximate the area under the curve y=2x-x^2 from x=1 to x=2

approximate the area under the curve from x=1 to x=2

a) using 4 equal inscribed rectangles

b) using 4 equal circumscribed rectangles

Nothing to it but to do it!

1) "equal" probably means equal length of the bases. The heights will be different.

2) Draw the bases [1.00,1.25][1.25,1.50][1.50,1.75][1.75,2.00]

3) Draw verticals at each of the five points, x = 1.00, 1.25, 1.50, 1.75, 2.00

3) Draw horizontals at each point where the the verticals intersect the graph. Extend the verticals, if necessary, until you have the four rectangles.

4) It really should be kind of obvious how to proceed form here. Just decide which side of the rectangle to use for inscribed and circumscribed.

Let's see what you get.