Evaluate the following definite integrals
`underset(0)overset(pi//2)intsin^(2)xdx`

Explanation

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

### Step 1: Use the identity for \(\sin^2 x\)
We can use the trigonometric identity:
\[ \sin^2 x = \frac{1 - \cos(2x)}{2} \]
This allows us to rewrite the integral.
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