JEE Mains · Maths · STD 12 - 7.2 definite integral
If \(\operatorname{I}(m, n)=\int_0^1 x^{m-1}(1-x)^{n-1} d x, m, n\gt0\), then \(I(9,14)+I(10,13)\) is
- A \(\mathrm{I}(19,27)\)
- B \(\mathrm{I}(9,1)\)
- C \(I(1,13)\)
- D \(\mathrm{I}(9,13)\)
Answer & Solution
Correct Answer
(D) \(\mathrm{I}(9,13)\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \mathrm{I}(\mathrm{m}, \mathrm{m})=\int_0^1 \mathrm{x}^{\mathrm{m}-1}(1-\mathrm{x})^{\mathrm{n}-1} d \mathrm{x} \\ & \text { Let } \mathrm{x}=\sin ^2 \theta \quad \mathrm{dx}=2 \sin \theta \cos \theta \mathrm{~d} \theta \\ & \mathrm{I}(\mathrm{m}, \mathrm{n})=2…
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