Go Back > Extra Stuff > Miscellaneous Math

Thread Tools
Old 2007-06-26, 19:11   #1
nuggetprime's Avatar
Mar 2007

12E16 Posts
Default Many CAS not able to solve integral

I tried(with wolfram integrator, mupad & derive) to solve this integral:

SIN(x)·(1 - COS(x))·

None of the three Computer Algebra Systems were able to do this correct(i set angle options). Can anybody help me?

nuggetprime is offline   Reply With Quote
Old 2007-06-26, 22:04   #2
alpertron's Avatar
Aug 2002
Buenos Aires, Argentina

5×269 Posts

Let x be the angle in degrees, so the angle in radians is:


So you want to integrate:

\sin \left(\frac{\pi}{180}x\right)\left(1-cos(\frac{\pi}{180}x)\right)\,=\, \sin \left(\frac{\pi}{180}x\right)-\sin \left(\frac{\pi}{180}x\right)\,cos(\frac{\pi}{180}x)

using standard sin and cos functions in radian.

Since \sin(2x) = 2\sin x \cos x we get:

\sin \left(\frac{\pi}{180}x\right)-\frac{1}{2}\sin \left(\frac{\pi}{90}x\right)

And its integral is:

-\frac{180}{\pi}\cos \left(\frac{\pi}{180}x\right)+\frac{45}{\pi}\cos \left(\frac{\pi}{90}x\right)

So the result in degrees is (using cosines in degrees):

-\frac{180}{\pi}\cos (x)+\frac{45}{\pi}\cos (2x)

I don't know the solution given by these packages but the difference between their results and the one I gave above should be a constant. Please notice that there are many ways to represent trigonometric identities so it is possible that two very different looking expressions are equal.

Last fiddled with by alpertron on 2007-06-26 at 22:15
alpertron is offline   Reply With Quote

Thread Tools

Similar Threads
Thread Thread Starter Forum Replies Last Post
Integral domain such that..... wildrabbitt Homework Help 2 2016-04-08 08:21
Need help with an integral Baztardo Homework Help 6 2011-04-10 22:17
Integral Variation flouran Information & Answers 6 2009-07-20 20:00
please help with an integral Andi47 Homework Help 3 2009-05-13 17:49
Challenging Integral Primeinator Homework Help 9 2008-12-23 16:40

All times are UTC. The time now is 05:56.

Mon Apr 12 05:56:22 UTC 2021 up 4 days, 37 mins, 1 user, load averages: 2.31, 2.08, 1.79

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.