AP EAMCET · Maths · Definite Integration
\(\int_0^1 \frac{x}{(1-x)^{3 / 4}} d x=\)
- A \(\frac{4}{5}\)
- B \(\frac{8}{15}\)
- C \(\frac{14}{5}\)
- D \(\frac{16}{5}\)
Answer & Solution
Correct Answer
(D) \(\frac{16}{5}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } I=\int_0^1 \frac{x}{(1-x)^{3 / 4}} d x, x=\sin ^2 \theta \Rightarrow d x=2 \sin \theta \cos \theta d \theta \\ & \because I=\int_0^{\pi / 2} \frac{\sin ^2 \theta}{\cos ^{3 / 2} \theta} \times 2 \sin \theta \cos \theta d \theta \\ & =2 \times…
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