Question

Estimate the area under the curve f(x) = x2 + 1 from x = 0 to x = 6 by using three circumscribed (over the curve) rectangles. Answer to the nearest integer.

Answer 1

1) split the range in three identical invervals of size [6 - 0] / 3 = 2

2) form three rectangles

2a) First rectangle: base 2, height f(2) = 2^2 + 1 = 5

area 1 = base * height = 2 * 5 = 10

2b) second rectangle: base 2, height f(2+2) = 4^2 + 1 = 17

area 2 = 2 * 17 = 34

2c) third rectangle: base 2 height f(4+2) = 6^2 + 1 = 37

area 3 = 2*37 = 74

3) total area = area 1 + area 2 + area 3 = 10 + 34 + 74 = 118