Question

using rectangles whose height is given by the value of the function at the midpoint of the rectangles base (the midpoint rule) estimate the area under the graph using 2 then 4 rectangles f(x)=x^2 between 0,1

Answer 1

F(x)=x^2

two rectangle from 0 1 so each rect is 1/2 wide
0 1/2 1
1/4 3/4

1/2 (F(1/4)+F(3/4)

Answer 2

thank you, what if im looking for a lower estimate

Answer 3

four rectangle
so each rect would be 1/4 wide
0 1/4 2/4 3/4 1
1/8 3/8 5/8 7/8
1/4 [F[1/8]+F[3/8]+F[5/8]+F[7/8]]