Evaluate : `int_0^(pi/2)cos^3xdx`

Explanation

To evaluate the integral \( \int_0^{\frac{\pi}{2}} \cos^3 x \, dx \), we can follow these steps:

### Step 1: Rewrite the Integral
We can express \( \cos^3 x \) as \( \cos x \cdot \cos^2 x \). We know that \( \cos^2 x = 1 - \sin^2 x \). Thus, we can rewrite the integral as:
\[ \int_0^{\frac{\pi}{2}} \cos^3 x \, dx = \int_0^{\frac{\pi}{2}} \cos x (1 - \sin^2 x) \, dx \]

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