Is this your question
Evaluate:
Hello,
(where )
So
Inverting the sum and the integral (using the proper theorems), we have :
where (known as Wallis integral in French..couldn't find it in English)
By a common method ( ) and an integration by parts, we get the recursive relation :
We can deduce this :
So if n is even,
And if n is odd,
So we have :
But hey, this is the power series for arcsin !!!
So finally, (I hope I didn't get wrong in the power series)
hi sir,
plz explain what I'(b) actually is and how do we differentiate a portion within the integration symbol with constant limits of integration........
I'm a precollege student preparing for an entrance exam.We were not introduced to these type of problems,still I have got such a problem in a test.I hope sincerely you people will definitely help me out in these kind of problems
thank you very much.
http://en.wikipedia.org/wiki/Leibniz_integral_rule
Well, it's a basic power series (google for it)
We know (geometric series) that if , then
Integrate from 0 to x :