Question

Given f (x) = √(7 + x) + 4 . Use the rectangle method to approximate the area on the interval [0, 8] using 4
rectangles. (Assume the graph goes through the midpoint of each rectangle.)

Answer 1

(sigma)M = (b-a) f((a+b)/2)
width:
(b-a)=2-0
(b-a)=4-2
(b-a)=6-4
(b-a)=8-6 =2
find the height:
f((a+b)/2)
(e.g. ([√(7 + a) + 4] + [√(7 + b) + 4])/2)

take the sum of "rectangles" (i.e. product of width and height)

rectangle method:
http://spiff.rit.edu/classes/phys317/lectures/num_integ2/num_integ2.html