# Reduction Formula

Printable View

• Mar 30th 2013, 07:14 AM
Amar124
Reduction Formula
Hey there, I've been struggling with this one for quite a while; so much so that I created an account on here so that I could ask for some help

I(n) = integral of ((e^sinx)(cosx)(sin^n x))

I need to show that it comes down to I(n) = e - n I(n-1)

The integral doesn't have any limits, but I'm pretty sure I need to integrate by parts, but I've tried all the different combinations for u and dv/dx and haven't gotten anywhere.

Thanks for the help :)
• Mar 30th 2013, 08:12 AM
HallsofIvy
Re: Reduction Formula
First make the substitution y= sin(x). What does that integral become? Now use integration by parts.
• Mar 30th 2013, 08:50 AM
Amar124
Re: Reduction Formula
Quote:

Originally Posted by HallsofIvy
First make the substitution y= sin(x). What does that integral become? Now use integration by parts.

Wow I never even thought of doing a substitution on a reduction formula question. I've been used to doing it by parts.

Yh that really simplifies things, thanks :)
• Mar 30th 2013, 10:06 AM
Amar124
Re: Reduction Formula
Quote:

Originally Posted by HallsofIvy
First make the substitution y= sin(x). What does that integral become? Now use integration by parts.

I get to I(n) = (y^n)(e^y) - n I(n-1)

In order for me to prove what I need to, I must show that (y^n)(e^y) = e which I'm pretty sure isn't the case. Any tips on what I can do?

Thanks :)
• Mar 31st 2013, 12:44 AM
jstefanov
Re: Reduction Formula
Ivanstefanov will write a c/c++ program/project for \$5, only on fiverr.com

I will write a C/C++ program/project.
I'm writing programs from more than 10 years also studied at the university ,math and computer science.I'm glad to help you with all i can for your homework ,assignment or project you want to write.