Find the value of the integral from 1 to 9 of x squared, dx using four rectangles of equal width, with each left end-point used to find the height of each rectangle.

Question

Find the value of  using four rectangles of equal width, with each left end-point used to find the height of each rectangle. (2 points)

A	2(1 + 9 + 25 + 49)
B	2(9 + 25 + 49 + 81)
C	0.5(1 + 9 + 25 + 49)
D	0.5(9 + 25 + 49 + 81)

Answer 1

The four rectangles of equal width are over the intervals

[1,3], [3,5], [5,7], [7,9].

Their height is the be calculated at the left end-points, so the heights are

1, 9, 25, 49.

Each interval has width 2, and therefore the answer is

2(1 + 9 + 25 + 49)