Question

Find the area of the region bounded by the given curves.
y=cos^3x,y=cosx,x=0,x=pi/2

Answer 1

\[\int\limits_{0}^{\frac{\pi}{2}}(\cos(x)-\cos^3(x)) dx \]

Answer 2

\[\sin(x)|_0^\frac{\pi}{2}- \int\limits_{0}^{\frac{\pi}{2}}\cos^2(x) \cos(x) dx\]
\[\sin(\frac{\pi}{2})-\sin(0)-\int\limits_{0}^{\frac{\pi}{2}} (1-\sin^2(x)) \cos(x) dx\]
\[1-0-\int\limits_{0}^{\frac{\pi}{2}}\cos(x) dx+\int\limits_{0}^{\frac{\pi}{2}}\sin^2(x) \cos(x)\]

Answer 3

see if you can get it from here

Answer 4

let me know if you run into trouble