Word Count : 256

---

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: \[ \sqrt{4x - x^2} = \sqrt{4 - (x-2)^2} \] this suggests a trigonometric substitution. Using \( x = _____ _______ _____ ____ ______.
____ ___ ____ _______ _________.
___ ____ _____ ___ ____ ___ ___ __________ __________ ________ ___ _______.
___ __________ __________ ____ ________ ________ ______ ______.
________ _______ __________ _________ _____.
_____ ______ ___ ___ ___ __________ _________ _______ _______.
_____ _________ ______ ___ ______ _____ _____ ___ ___.
___ _________ _____ ________ _____ _____ _____ ___ _____ _____ _______ _________.
_________ __________ ____ __________ ________ _____ ________.
____ ___ ______ __________ ___ ___ ______ ______.
________ _________ _____ _________ ________ ________ _______.
_________ __________ _____ _______ _______ _________ ________ __________ _____ __________ ________ ______.
______ __________ _____ _____ ________ _______ __________ ______ ___.
___ ______ _____ _________ _____.
________ _____ _______ ________ ____ _________ __________ ______ _________.
_______ ___ __________ _______ _____ _____.
_________ ________ ____ ___ ________ _________.
_______ ____ _________ ________ __________ ________.
______ _________ ___ ___ _______ ________ _____ __________ _________.
________ ________ ____ _____ _________ ____.
________ ___ _____ ____ ____ ______ __________ _____ __________ _____.
______ ______ _______ ___ ______ _______.
______ ____ ______ _____ ___ ____ ______ ____ ___.
______ ____ _____ _______ ___ __________ ______.
_____ ____ ___ _________ _____ ________ ______.
___ _______ _______ _________ __________ __________ ____ ______ ________.
______ _____.
Get Full Answer on WhatsApp