Chapter 8.5, Problem 10QR

To determine

To find the Riemann sums ${\displaystyle \sum \frac{\sqrt{3}}{4}\left({\sin }^2{x}_k\right)}\Delta x$ by converting into integrals.

Answer to Problem 10QR

The limit is ${\displaystyle \underset{0}{\overset{7}{\int }}\frac{\sqrt{3}}{4}\left({\sin }^{2}x\right)dx}$

Explanation of Solution

Given information: The Riemann sums on [0, 7] is ${\displaystyle \sum \frac{\sqrt{3}}{4}\left({\sin }^2{x}_k\right)}\Delta x$

Calculation :

The limit of the function is:

  ${\displaystyle \underset{0}{\overset{7}{\int }}\frac{\sqrt{3}}{4}\left({\sin }^{2}x\right)dx}$ .