Question

Consider the region in the 1st quadrant enclosed by the graphs f(x)=cos(pi/8x) and g(x)=sin(pi/8x). Find the volume of the solid that is formed by rotating this region about the x-axis!

Answer 1

sin = cos at pi/4
therefore at x=2 --> pi/8 *2 = pi/4

outer radius is cos function
inner radius is sine function
\[V =\pi \int\limits_{0}^{2}\cos^{2} (\pi/8x) - \sin^{2}(\pi/8 x) dx\]
use trig identity: cos^2 - sin^2 = cos(2x)
\[\rightarrow \pi \int\limits_{0}^{2}\cos(\pi/4 x) dx\]