Question

The value of `int_(-pi)^pi sin^3x cos^2x  "d"x` is ______.

Answer 1

The value of `int_(-pi)^pi sin^3x cos^2x  "d"x` is 0.

Explanation:

Let I = `int_(-pi)^pi sin^3x cos^2x  "d"x`

Let f(x) = sin³x cos²x

f(–x) = sin³(– x) cos²(– x)

= – sin³x cos²x

= – f(x)

∴ `int_(-pi)^pi sin^3 x cos^2 x  "d"x` is an odd function

∴ I = 0