Chapter 8.5, Problem 3QR

To determine

To find the value of the integral ${\displaystyle \underset{\pi /4}{\overset{\pi /2}{\int }}\sin xdx}$ by finding the anti-derivative.

Answer to Problem 3QR

The value of the integral is 0.7071.

Explanation of Solution

Given information: ${\displaystyle \underset{\pi /4}{\overset{\pi /2}{\int }}\sin xdx}$

Formula used: ${\displaystyle \int \sin xdx}=-\cos x$

Calculation :

The given integral is

  ${\displaystyle \underset{\pi /4}{\overset{\pi /2}{\int }}\sin xdx}=-{\left[\cos x\right]}_{\pi /4}^{\pi /2}=\frac{1}{\sqrt{2}}=0.7071$

Hence, the value of the integral is 0.7071.