`int_0^1sqrt((1-x)/(1+x))dx=` `(pi)/2` (b) `(pi)/2-1` (c) `(pi)/2+1` (d) `pi+1`

Explanation

To solve the integral \( \int_0^1 \sqrt{\frac{1-x}{1+x}} \, dx \), we will use a trigonometric substitution. Let's go through the steps:

### Step 1: Substitution
Let \( x = \cos(2\theta) \). Then, we differentiate to find \( dx \):
\[ dx = -2\sin(2\theta) \, d\theta \]

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