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Thanks op=op Got it \int_{0}^{1}x^m.(1-x)^n dx = \frac{m!.n!}{(m+n+1)!} Proof:: Let I_{m,n} = \int (1-x)^n . x^m dx = \frac{n}{m+1}\int (1-x)^{n-1}.x^{m+1}dx = \frac{n}{m+1}.I_{n-1,m+1} = \frac{(n).(n-1)}{(m+1).(m+2)}I_{n-2,m+2} = \frac{(n).(n-1).................1}{(m+1).(m+2)..............(m+n)}I_{...

value of

where

\left(x^{2010}-1\right).\left( x^{2010}+1 \right) = ? I think the formula is: \left(1+x^2+x^4+x^6+............+x^{2008} \right).\left(x^{2010}+1\right) = 2010x^{2008} Thanks friends I have got the answer. But i did not understand the line \left(1+x^2+x^4+x^6+............+x^{2008} \right).\left(x^{2...

Calculate value of

How can I calculate without using Gamma function

Thanks.

My Solution:: We can write

So equation is

Now How Can I Solve after that

Thanks

Let denote the set of all real values of such that



Then no. of element in

Thanks moderator got it

Thanks arno and moderator

for , Then the possible number of different integral values which can take is

20 children are standing in a line outside a ticket window . 10 of them have one rupee coin each and 10 have two rupee coin each and the entry ticket is priced Rupee 1. if all arrangements of 2o children are equally likely , find probability that 10th child will be first to wait for change

The number of integer ordered pairs of the equation

Thanks Arno, I have solved like this way. Let \displaystyle\bf{I=\frac{\sin x}{5+4\cos x}}\; , Then \displaystyle\bf{\frac{dI}{dx}=\frac{(5+4\cos x).(\cos x)-\sin x.(-4\sin x)}{(5+4\cos x)^2}} \displaystyle\bf{\frac{dI}{dx}=\frac{5\cos x+4}{(5+4\cos x)^2}=\frac{5}{4}.\frac{(4\cos x+5)}{(5+4\cos x)^...