JEE Mains · Maths · STD 12 - 7.2 definite integral
Let \(\beta(m, n)=\int_0^1 x^{m-1}(1-x)^{n-1} d x, m, n>0\). If \(\int_0^1\left(1-x^{10}\right)^{20} d x=a \times \beta(b, c)\), then \(100(a+b+x)\) equals
- A \(1021\)
- B \(1120\)
- C \(2012\)
- D \(2120\)
Answer & Solution
Correct Answer
(D) \(2120\)
Step-by-step Solution
Detailed explanation
\( I=\int_0^1 1 \cdot\left(1-x^{10}\right)^{20} d x \) \( x^{10}=t \) \( x=t^{1 / 10} \) \( d x=\frac{1}{10}(t)^{-9 / 10} d t \) \( I=\int_0^1(1-t)^{20} \frac{1}{10}(t)^{-9 / 10} d t \) \( I=\frac{1}{10} \int_0^1 t^{-9 / 10}(1-t)^{20} d t \)…
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