Help with ycosx ysin2X x OX pi 2 Solution The curves inters

Solution

The curves intersect at two points between 0 and pi/2, so the total area is the sum of two integrals. The area ends up being: Integral of (cos(x)-sin(2x)) dx from x = 0 to pi/6 PLUS Integral of (sin(2x) - cos(x)) dx from x = pi/6 to x = pi/2 Note: the reason the second integral is (sin(2x)-cos(x)) is because sin(2x) is higher than cos(x) between x = pi/6 and x = pi/2. In the first integral, cos(x) is higher than sin(2x) so the integral was (cos(x)-sin(2x)). The integral of (cos(x)-sin(2x)) dx from x = 0 to pi/6 is 1/4, and the integral of (sin(2x)-cos(x))dx from x = pi/6 to x = pi/2 is 1/4. Then the total area enclosed between the two curves between x = 0 and pi/2 is 1/4+1/4 = 1/2