Reimann Sum Integral Estimation

Question

Use the table to estimate ∫ 0 to 40 f(x)dx. Assume that f(x) is an increasing function.

x | 0 | 10 | 20 | 30 | 40 |

f(x) | 370 | 400 | 430 | 470 | 490 |

Estimate the integral using the average of left- and right-hand sums

∫ 0 to 40 f(x)dx ≈

Answer 1

The area of each rectangle is width multiplied by height

LH Sum:

10(370) + 10(400) + 10(430) + 10(470)

RH Sum:

10(400) + 10(430) + 10(470) + 10(490)

As mentioned, you can then estimate the answer by averaging the LH and RH together.