Consider the following table:

Question

x 0 4 8 12 16 20

f(x) 38 37 35 31 22 3

(a) Use this data and a left-endpoint Riemann sum to estimate the integral:

∫²⁰₀ f(x)dx≈

(b) Use this data and a right-endpoint Riemann sum to estimate the integral:

∫²⁰₀ f(x)dx≈

Answer 1

(a) Left Reimann Sum:

∫₀²⁰f(x)dx ≈ (4−0)38+(8−4)37+(12−8)35+(16−12)31+(20−16)22 = 652.

(b) Right Reimann Sum:

∫₀²⁰f(x)dx ≈ (4−0)37+(8−4)35+(12−8)31+(16−12)22+(20−16)3=512.