$\int\frac{dx}{\sqrt{2x-x^2}}$ is equal

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Definite Integration

Question:

$\int\frac{dx}{\sqrt{2x-x^2}}$ is equal to

Options:

sin^–1 (1 - x) + c

– cos^–1(1 – x) + c

sin^-1 (x – 1) + c

cos^-1 (x – 1) + c

Correct Answer:

sin^-1 (x – 1) + c

Explanation:

Let $I=\int\frac{dx}{\sqrt{1-(x^2-2x+1)}}=\int\frac{dx}{\sqrt{1-(x-1)^2}}=sin^{-1}(\frac{x-1}{1})+c$.

Hence (C) is the correct answer.