Evaluate `int_(0)^(pi)sin^(3)x*cos^(4)xdx`

Explanation

To evaluate the integral \( I = \int_{0}^{\pi} \sin^3 x \cos^4 x \, dx \), we can follow these steps:

### Step 1: Rewrite the integral
We start by rewriting \( \sin^3 x \) as \( \sin x \cdot \sin^2 x \):
\[ I = \int_{0}^{\pi} \sin x \cdot \sin^2 x \cdot \cos^4 x \, dx \]
Using the identity \( \sin^2 x = 1 - \cos^2 x \), we can substitute:
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