Question

Describe strategy for solving the type of integral given.

$\int {\sin }^{m}x{\cos }^{n}xdx$, both$m,n$even

Short answer

Write${\sin }^{m}x={\sin }^{2}x{\sin }^{m-2}x$or${\cos }^{n}x={\cos }^{2}x{\cos }^{n-2}x$

Step-by-step solution

Step 1. Given information

Integral is$\int si{n}^{m}xco{s}^{n}xdx$, both$m,n$even

Step 2. Explanation

Consider the integral $\int {\sin }^{m}x{\cos }^{n}xdx$, both $m,n$even

Use the formula ${\sin }^{2}x=1-{\cos }^{2}x$or${\cos }^{2}x=1-{\sin }^{2}x$