AP EAMCET · Maths · Definite Integration
\(\int_{-1}^1 \frac{\sqrt{1+x+x^2}-\sqrt{1-x+x^2}}{\sqrt{1+x+x^2}+\sqrt{1-x+x^2}} d x\) is equal to
- A \(\frac{3\pi}{2}\)
- B \(\frac{\pi}{2}\)
- C \(0\)
- D \(-1\)
Answer & Solution
Correct Answer
(C) \(0\)
Step-by-step Solution
Detailed explanation
\(I=\int_{-1}^1 \frac{\sqrt{1+x+x^2}-\sqrt{1-x+x^2}}{\sqrt{1+x+x^2}+\sqrt{1-x+x^2}} d x\) Let \(f(x)=\frac{\sqrt{1+x+x^2}-\sqrt{1-x+x^2}}{\sqrt{1+x+x^2}+\sqrt{1-x+x^2}}\) Replacing \(x\) by \(-x\), we get…
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