Find the Definite Integrals : `int_0^(pi/2) sin^2x cos^3x dx `

Explanation

To solve the definite integral \( I = \int_0^{\frac{\pi}{2}} \sin^2 x \cos^3 x \, dx \), we will use the method of substitution.

### Step-by-Step Solution:

1. **Substitution**:
Let \( z = \sin x \). Then, the differential \( dz = \cos x \, dx \) or \( dx = \frac{dz}{\cos x} \).

2. **Change the Limits**:
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