TS EAMCET · Maths · Indefinite Integration
\(\int \frac{d x}{\sqrt{x-x^2}}\) is equal to
- A \(2 \sin ^{-1} \sqrt{x}+C\)
- B \(2 \sin ^{-1} x+C\)
- C \(2 x \sin ^{-1} x+C\)
- D \(\sin ^{-1} \sqrt{x}+C\)
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 \(\quad \sqrt{x}=\sin \theta\)…
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