Evaluate the following integral: `int_(-pi//2)^(pi//2)sin^9x\ dx`

Explanation

`int_{frac{-x}{2}}^{frac{pi}{2}} sin ^{9} x d x`



consider `f(x)=sin ^{9} x`


Consider, `f(-x)=sin ^{9}(-x)=-sin ^{9} x=-f(x) `


Here f(x) is an odd function

`
therefore,

int_{frac{-x}{2}}^{frac{x}{2}} sin ^{9} x d x=0`

`