Answer to Question #99962 in Calculus for Jericho cruz

Question

Evaluate the definite integral

Integral of sin^6xcos^8xdx

upper is pi/2
lower is 0

Answer 1

There is a formula for evaluating this kind of integral:

$\int_{0}^{\frac{\pi}{2}} (Sin^mxCos^nx)dx =\frac{[(m-1)(m-3)...1][(n-1)(n-3)..1]}{[(m+n)(m+n-2)...2]}*\frac{\pi}{2}$

When both m and n are even.

Here, we have $m=6,n=8$

Put the value of m and n in the above formula, we will get the value of required integral as:

$\frac{[5.3.1][7.5.3.1]}{[14.12.10.8.6.4.2]}*\frac{\pi}{2}$

$=\frac{15*105}{645120}*\frac{\pi}{2}$

$=\frac{1575}{645120}*\frac{\pi}{2}$

$=0.00122\pi$