Chapter 8.5, Problem 8QR

To determine

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

Answer to Problem 8QR

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

Explanation of Solution

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

Calculation :

The limit of the function is:

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