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The value of is see image if scrip not supported

  The value of   is
see image if scrip not supported

Question Image
Grade:12

1 Answers

Latika Leekha
askIITians Faculty 165 Points
6 years ago
Hello student,
The given term is
\frac{5050 \int_{0}^{1}(1-x^{50})^{100}dx}{\int_{0}^{1}(1-x^{50})^{101}dx}
= \frac{5050I_{100}}{I_{101}}
I101 = \int_{0}^{1}1.(1-x^{50})^{101}dx
= x(1-x^{50})^{101} + 100\int_{0}^{1}50 (1-x^{50})^{100}.x^{50}dx
= -5050\int_{0}^{1}\left [ (1-x^{50}) \right ]^{100}((1-x^{50})-1)dx
= -5050(I101 - I100)
So, 5051 I101 = 5050 I100
So, 5050 (I100/I101) = 5051

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