TS EAMCET · Maths · Definite Integration
\(\int_0^1 x^{3 / 2} \sqrt{1-x} d x\) is equal to
- A \(\frac{\pi}{6}\)
- B \(\frac{\pi}{9}\)
- C \(\frac{\pi}{12}\)
- D \(\frac{\pi}{16}\)
Answer & Solution
Correct Answer
(D) \(\frac{\pi}{16}\)
Step-by-step Solution
Detailed explanation
Let \(I=\int_0^1 x^{3 / 2} \sqrt{1-x} d x\) Put \(x=\sin ^2 \theta \Rightarrow d x=2 \sin \theta \cos \theta d \theta\)…
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