Evaluate : `int_(0)^(1) cos^(-1) dx`

Explanation

To evaluate the integral \( I = \int_{0}^{1} \cos^{-1}(x) \, dx \), we will use a substitution method and integration by parts. Here’s the step-by-step solution:

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

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