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To evaluate the integral \[ I = \int_{0}^{4} \frac{dx}{\sqrt{4x - x^2}} \] using Beta and Gamma functions, follow these steps: ### Step 1: Recognizing the Integral in a Standard Form Rewriting the denominator: \[ \sqrt{4x - x^2} = \sqrt{4 - (x-2)^2} \] _______ _________ ___ _________ __________ ___ _____ ____.
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