Let R be the region in the first quadrant enclosed by the graph of y=2cosx, the x-axis, and the y-axis, how do you find the area of the region R?

Jan 14, 2018

$2 \text{ sq units}$

Explanation:

graph{2cosx [-2.5, 7.5, -2.3, 2.7]}

the graph shows $y = 2 \cos x$

to find the required are we need the x-coordinates where the graph crosses the x-axis in the region required

$x = 0 , \frac{\pi}{2}$

$A = {\int}_{0}^{\frac{\pi}{2}} 2 \cos x \mathrm{dx}$

$= {\left[2 \sin x\right]}_{0}^{\frac{\pi}{2}}$

$= \left[2 \sin \left(\frac{\pi}{2}\right)\right] - \left[2 \sin 0\right]$

$= 2 \times 1 = 2$