JEE Mains · Maths · STD 12 - 7.2 definite integral
If \(I _{1}=\int \limits_{0}^{1}\left(1- x ^{50}\right)^{100} dx\) and \(I _{2}=\int \limits_{0}^{1}\left(1- x ^{50}\right)^{101} dx\) such that \(I_{2}=\alpha I_{1}\) then \(\alpha\) equals to
- A \(\frac{5050}{5051}\)
- B \(\frac{5050}{5049}\)
- C \(\frac{5049}{5050}\)
- D \(\frac{5051}{5050}\)
Answer & Solution
Correct Answer
(A) \(\frac{5050}{5051}\)
Step-by-step Solution
Detailed explanation
\(I _{1}=\int_{0}^{1}\left(1- x ^{50}\right)^{100} dx\) and \(I _{2}=\int_{0}^{1}\left(1- x ^{50}\right)^{101} dx\) and \(I _{1}=\lambda I _{2}\) \(I _{2}=\int_{0}^{1}\left(1- x ^{50}\right)^{101} dx\)…
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