y1 and y112x interval x01 find the area bounded between thes

Solution

The trouble is that the graph of cosx intersects with that of sin2x at two points. After the first point the value of sin2x becomes higher than cosx. Since the areas are actually equal but of opposite signs, you are getting a net result as zero.

First find out the points of intersection of the two curves bby equating them
thus cosx = sin2x
this will yiled two values for x, i.e. x=pi/2 or x=pi/6
from x=0 to pi/6 you integrate as you have done.
from x=pi/6 to pi/2, integrate with oppposite sign i.e. integral of sin2x-cosx.
you would get 1/4 for each and the sum would come out to be 1/2