f(x)=2x+5

a=0

b=4.

Approximate the area under the curve with 4 rectangles using the left-hand endpoint, the right-hand endpoint, and the midpoint. The actual area is 36. Which approximation gave the closest estimate?

Using the left-hand endpoint, the approximate area is ___?

Using the right-hand endpoint, the approximate area is ___?

And the midpoint?

Guest Apr 25, 2017

#1**+2 **

Using the left-hand endpoint, the approximate area is f(a)*(b - a) = 5*4 → 20

Using the right-hand endpoint, the approximate area is f(b)*(b - a) = 13*4 → 52

Using the midpoint, the area is (f(a) + f(b))/2 * (b - a) = (5 + 13)/2 * 4 → 9*4 → 36

(Not clear why you mentioned 4 rectangles!).

Alan
Apr 25, 2017