Chapter 8.5, Problem 6QR

To determine

To find the Riemann sums ${\displaystyle \sum \left(2\pi (x_k+2)(\sin x_k)\Delta x\right)}$ by converting into integrals.

Answer to Problem 6QR

The limit is ${\displaystyle \underset{0}{\overset{7}{\int }}\left(2\pi (x+2)\sin x\right)dx}$ .

Explanation of Solution

Given information: The Riemann sums on [0, 7] is ${\displaystyle \sum \left(2\pi (x_k+2)(\sin x_k)\Delta x\right)}$

Calculation :

The limit of the function is:

  ${\displaystyle \underset{0}{\overset{7}{\int }}\left(2\pi (x+2)\sin x\right)dx}$ .