Question

Consider the following table:

x 0 3 6 9 12 15
f(x) 37 36 34 30 21 3
(a) Use this data and a left-endpoint Riemann sum to estimate the integral:
∫^{15}_0 f(x)dx≈

(b) Use this data and a right-endpoint Riemann sum to estimate the integral:
∫^{15}_0 f(x)dx≈

(c) Find the average of the left- and right-endpoint Riemann sums to estimate the integral:
∫^{15}_0 f(x)dx≈

Answer 1

for the left sum, we have

left = 3(37+36+34+30+21)

similarly for the right

and then (left+right)/2