How do i find and what is the recurrence formula for (x^n)(1+x)^1/2.dx between the x terminals 0 and -1 ? Thanks Nath
First you problably mean that,Originally Posted by nath_quam
otherwise the function is not defined, which means that ,
makes no sense at all!.
Assuming you mean,
Use integration by parts,
let, then, and, then,
Thus,
Thus,
The trick is to express,
as,
Thus,
Working with the integral we have,
=
Let,
Then, as we have shown,
Which is,
Thus,
Thus,
Thus,
Thus, the recurrence formula is,
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Credits:
I learend the box trick from Soroban
Let:Originally Posted by CaptainBlack
.
Now we are going to use integration by parts, which has the schema:
.
Here we let: , and , so:
,
and:
.
So
.
Putting the limits back in:
.
Simplifying:
.
So the recurrence relation for is:
RonL
(you will need to check this carefully as there are too many steps to
guarantee there is no mistake)