Question

Find the area under the curve y=5(cosx) and above y=5(sinx) for 0<x<pi

Answer 1

Sketch a graph of the two functions between 0 and pi.
Note that cos x is above sin x only between x = 0 and x = pi/4
so
we have 5 times integral from 0 to pi/4 of cos x dx - sin x dx
cos x dx --> sin x 0 to pi/4 = .5 sqrt 2
sin x dx = -cos x 0 to pi/4= -.5sqrt 2 +1
cos x dx - sin x dx --> sqrt 2 - 1
times 5 = 5 sqrt 2 - 5
or about 7.07 - 5 = 2.07