help@askiitians.com

+91-705-589-3577

Integral Calculus> The value of is see image if scrip not su...

question mark

The value of is
see image if scrip not supported

Ranjit Pal , 10 Years ago

Grade 12

1 Answers

Latika Leekha

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

Approved

Last Activity: 10 Years ago

LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

Full Live Access

Study Material

Live Doubts Solving

Daily Class Assignments

The area of a square field is 640000cm².what is its area in hectares

integral calculus

1 Answer Available

Last Activity: 3 Years ago

Please solve this integration. I am facing difficulty in it
How to solve this. Please solve anyone. Humble request

integral calculus

1 Answer Available

Last Activity: 3 Years ago

Using laplace transform, solve d²y/dt²+ dy/dt = t² +2t given that y=4 and y’=-2 and t=0

integral calculus

1 Answer Available

Last Activity: 3 Years ago

If 4th term of an A.p is zero, show that the 8th term is double the 6th term

integral calculus

1 Answer Available

Last Activity: 4 Years ago

View all Questions