
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
August 17th, 2012, 10:54 AM  #1 
Senior Member Joined: Aug 2012 From: New Delhi, India Posts: 157 Thanks: 0  Evaluation of (sin x)^m (cos x)^n dx
Given the values of m & n how would you evaluate without means of Gamma function? 
August 17th, 2012, 11:49 AM  #2 
Math Team Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions  Re: Evaluation of (sin x)^m (cos x)^n dx Just a Hint I would first rewrite is like this using integrating by parts I would continue until I get sin(x) 
August 17th, 2012, 01:41 PM  #3  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: Evaluation of (sin x)^m (cos x)^n dx Hello, Rejjy! Quote: [color=beige]. . [/color] [color=beige]. . [/color] [color=beige]. . [/color] [color=beige]. . [/color] ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ [color=beige]. . . . . . [/color] [color=beige]. . . . . . [/color]  
August 18th, 2012, 01:19 AM  #4 
Senior Member Joined: Sep 2009 From: Wisconsin, USA Posts: 227 Thanks: 0  Re: Evaluation of (sin x)^m (cos x)^n dx
What about something along the lines of m=7/2 and n=3/2.

August 18th, 2012, 07:46 AM  #5 
Senior Member Joined: Aug 2012 From: New Delhi, India Posts: 157 Thanks: 0  Re: Evaluation of (sin x)^m (cos x)^n dx
And what if m and n are very large? I have a book that states the following result. Also, it says to multiple the above by if both m and n are even. @The_Fool Agreed, that is an interesting question. However, I am not aware if the above result holds for fractional m & n. It seems like it won't. Regards, Rejjy 18Aug2012 21:16 IST 
August 18th, 2012, 09:10 AM  #6  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Evaluation of (sin x)^m (cos x)^n dx Quote:
where is the complete elliptic integral of the first kind and is the gamma function. Balarka .  
August 18th, 2012, 09:22 AM  #7 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Evaluation of (sin x)^m (cos x)^n dx
Now for the original problem, I would prefer zaidalyafey's method : if then, where which is elementary and easy to calculate. Balarka . 
August 18th, 2012, 02:24 PM  #8  
Senior Member Joined: Sep 2009 From: Wisconsin, USA Posts: 227 Thanks: 0  Re: Evaluation of (sin x)^m (cos x)^n dx Quote:
 
August 18th, 2012, 10:22 PM  #9  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Evaluation of (sin x)^m (cos x)^n dx Quote:
 
August 19th, 2012, 01:16 AM  #10 
Senior Member Joined: Sep 2009 From: Wisconsin, USA Posts: 227 Thanks: 0  Re: Evaluation of (sin x)^m (cos x)^n dx
Well, I don't think that's right anyway since that integral is real: I used the beta function instead of the gamma function. While beta can be defined by gamma, it can stand on it's own without it in several other forms. 

Tags 
cos, evaluation, sin 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
int(1/n^n) evaluation  mathbalarka  Calculus  5  February 18th, 2013 12:53 AM 
Evaluation of a Series  rnck  Real Analysis  7  July 12th, 2012 12:33 PM 
Integration evaluation  jakeward123  Calculus  3  March 2nd, 2011 08:54 AM 
Trig evaluation  mnangagwa  Calculus  9  March 16th, 2009 08:23 PM 
Evaluation Help  Soha  Algebra  2  February 3rd, 2007 06:33 AM 