AP EAMCET · Maths · Indefinite Integration
\(0 < \mathrm{x} < 1, \int \frac{d x}{\sqrt{x^2-x^5}}=\frac{1}{3} \log |f(x)|+C\), then \(f\left(\frac{1}{2}\right)=\)
- A \(\frac{(\sqrt{8}-\sqrt{7})}{(\sqrt{8}+\sqrt{7})}\)
- B \(\frac{(\sqrt{8}+\sqrt{7})}{(\sqrt{8}-\sqrt{7})}\)
- C \(2(\sqrt{8}-\sqrt{7})\)
- D \(2(\sqrt{8}-\sqrt{7})^2\)
Answer & Solution
Correct Answer
(A) \(\frac{(\sqrt{8}-\sqrt{7})}{(\sqrt{8}+\sqrt{7})}\)
Step-by-step Solution
Detailed explanation
\(\int \frac{d x}{\sqrt{x^2-x^5}}=\int \frac{d x}{x \sqrt{1-x^3}}=\int \frac{x^2 d x}{x^3 \sqrt{1-x^3}}\)…
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