Solution:

Before we proceed integration we first check if the function is odd.

Let, \(f(x)=\sin^3x\cos^2x\)

Put x = -x

\(f(-x)=\sin^3(-x)\cos^2(-x)\) 

= -\(\sin^3x\cos^2x\)

= f(x)

This confirms that the function involved in integration is odd. Hence

\(\int_{-1}^1\sin^3x\cos^2x\operatorname dx\) = 0