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TS EAMCET · Maths · Indefinite Integration

\(\int \frac{d x}{\sqrt{x-x^2}}\) is equal to

  1. A \(2 \sin ^{-1} \sqrt{x}+C\)
  2. B \(2 \sin ^{-1} x+C\)
  3. C \(2 x \sin ^{-1} x+C\)
  4. D \(\sin ^{-1} \sqrt{x}+C\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(2 \sin ^{-1} \sqrt{x}+C\)

Step-by-step Solution

Detailed explanation

Let \(\begin{aligned} I & =\int \frac{d x}{\sqrt{x-x^2}} \\ & =\int \frac{1}{\sqrt{x}} \times \frac{d x}{\sqrt{1-x}}\end{aligned}\) Put \(\quad \sqrt{x}=\sin \theta\)…