Answer to Question #117678 in Calculus for Lizwi

Question

Find the area bounded by y=cosx, the x-axis and between x=−π/2 to x=π/2. Draw a sketch for yourself to help you find the integral.

Answer 1

The region bounded by $y=cosx$ , $x$−axis and between $y = -\frac{\pi}{2}$ and $y = \frac{\pi}{2}$ is the region below the curve as shown in figure:

Hence Area of required region is

$A = \int_{-\pi/2}^{\pi/2} y dx = \int_{-\pi/2}^{\pi/2} cos(x)dx \\ =sin(x)|_{-\pi/2}^{\pi/2} = -sin(-pi/2) +sin(pi/2) = -(-1)+1 = 2$