Question

Use the Midpoint Rule, with n = 4, to approximate the area bounded by f(x) = x^3-10x^2+25x and the x-axis between x = 0 and x = 5.

Answer 1

i found that delta x = 5/4, but i kinda forgot how to use the midpoint rule.

Answer 2

ok each rectangle (delta x) = (b-a)/n = (5-0)/4 = 5/4 long
now you need to find the height of each rectangle at its point.

So find the height of the first rectangle at (5/4)/2 = 5/8 by plugging in 5/8 into f(x) and multiply that by delta x.
Do the same for the 4 rectangles. The next midpoint will be at x= 5/4 + 5/8 = 15/8

Answer 3

sorry meant to say "now you need to find the height of each rectangle at its midpoint." in the second line

Answer 4

why do you divide 5/4 by 2? is it because it's midpoint?

Answer 5

Exactly, the midpoint is halfway to 5/4, so divide it by 2

Answer 6

ohhh okay, thanks :)

Answer 7

For the subsequent midpoints, just add 5/8 to whatever the starting point of the rectangle is

Answer 8

ok, thanks. my math teacher didn't really "explain" this stuff :/