AP EAMCET · Maths · Definite Integration
\(\int_0^1 x^{5 / 2}(1-x)^{3 / 2} \mathrm{~d} x=\)
- A \(\frac{5 \pi}{256}\)
- B \(\frac{3 \pi}{256}\)
- C \(\frac{3 \pi}{128}\)
- D \(\frac{5 \pi}{128}\)
Answer & Solution
Correct Answer
(B) \(\frac{3 \pi}{256}\)
Step-by-step Solution
Detailed explanation
\( \int_0^1 x^{5/2}(1-x)^{3/2} \mathrm{~d} x = B(5/2+1, 3/2+1) = B(7/2, 5/2) \) \( = \frac{\Gamma(7/2)\Gamma(5/2)}{\Gamma(7/2+5/2)} = \frac{\Gamma(7/2)\Gamma(5/2)}{\Gamma(6)} \)…
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