AP EAMCET · Maths · Definite Integration
\(\int_{1 / 5}^{1 / 2} \frac{\sqrt{x-x^2}}{x^3} d x=\)
- A \(\frac{21}{2}\)
- B \(\frac{14}{3}\)
- C \(\frac{7}{3}\)
- D \(\frac{7}{2}\)
Answer & Solution
Correct Answer
(B) \(\frac{14}{3}\)
Step-by-step Solution
Detailed explanation
\(\int_{1 / 5}^{1 / 2} \frac{\sqrt{x-x^2}}{x^3} d x = \int_{1 / 5}^{1 / 2} \frac{\sqrt{1-x}}{x^{5/2}} d x\) Let \(x = \sin^2 \theta \Rightarrow d x = 2 \sin \theta \cos \theta d\theta\)…
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