AP EAMCET · Maths · Indefinite Integration
If \(\int \frac{d x}{(1+\sqrt{x}) \sqrt{x-x^2}}=\frac{A \sqrt{x}}{\sqrt{1-x}}+\frac{B}{\sqrt{1-x}}+C\), where \(C\) is real constant, then \(A+B\) equals to
- A \(3\)
- B \(0\)
- C \(1\)
- D \(2\)
Answer & Solution
Correct Answer
(B) \(0\)
Step-by-step Solution
Detailed explanation
Given, \[ \int \frac{d x}{(1+\sqrt{x})\left(\sqrt{x^2-x^2}\right)}=\frac{A \sqrt{x}}{\sqrt{1-x}}+\frac{B}{\sqrt{1-x}}+c \] On differentiating both sides, we get…
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