Sketch the region enclosed by the given curves and find its area. y=cosx,y=4×21
Sketch the region and find the enclosed area.
i) The sketch of the region
The area A of the region bounded by the curves and the lines is
The point of intersection occurs when both equations are equal to each other, that is,
So at point of intersection,
By quadratic formula thus Thus by trial and error (in view of the graph) points of intersection are at and . The region is sketched in the following figure. We may also directly use the graph generated by some graphing utility to find the points of intersections.
Here, when . Therefore, let’s assume that
Therefore, the required area is
Compute the integral using the standard integration rule.
Evaluate the integral by plugging the upper and the lower limits of integration.