Talk:List of integrals of trigonometric functions

From Wikipedia, the free encyclopedia

Some suggestion. Shouldn't we name this like List of Integrals involing trigonometric functions or short, List of Integrals with trigonometric functions. Use of parentheses looks like disambiguation. -- Taku 15:24 27 May 2003 (UTC)

"List of integrals of trigonometric functions". And a lower case "i" for "integrals" too! -- Tarquin 15:30 27 May 2003 (UTC)
Either will be fine with me. -- schnee

The section titles here look kind of wordy and redundant. The user probably knows he's looking at integrals of trigonometric functions. You could probably get by with just 'Integrals containing only sin', etc. --67.137.24.115 01:11, 21 November 2006 (UTC)

Is there a mistake in \int\frac{\sin^n cx\;dx}{\cos^m cx} = \frac{\sin^{n-1} cx}{c(m-1)\cos^{m-1} cx}-\frac{n-1}{n-1}\int\frac{\sin^{n-1} cx\;dx}{\cos^{m-2} cx} \qquad\mbox{(for }m\neq 1\mbox{)}\,\!? Especially in the \frac{n-1}{n-1} part. --Telempe 10:35, 18 February 2007 (UTC)

Fixed --RDBury (talk) 03:47, 8 March 2008 (UTC)

Contents

[edit] Derivations

Shouldn't we put the derivations/proofs for at least the more basic of these formulas? Kr5t 22:58, 7 March 2007 (UTC)

[edit] + C

Since these are all improper integrals, shouldn't each of these end in + C. It's not noverly important, but text books still do it, and it would be technically correct, which is the best kind of correct. . . . 10:27, 30 June 2007 (UTC)

The + c is important for consistency. For example integrating 2cosxsinx two different ways gives sin2x and − cos2x, both are correct but without the + c you get sin2x = − cos2x, which is wrong. I'm going to try to add the +c's and change the c's that are already there to a's to avoid collision. —Preceding unsigned comment added by RDBury (talk • contribs) 04:02, 8 March 2008 (UTC)

[edit] Removed cot/tan section

I removed the cot and tan section. The only integral in it trivially simplified to another integral in this page.--RDBury (talk) 06:31, 8 March 2008 (UTC)

[edit] Deletions

I'm removing

\int\sqrt{1 - \sin{x}}\,dx = \int\sqrt{\operatorname{cvs}\,{x}}\,dx = 2 \frac{\cos{\frac{x}{2}} + \sin{\frac{x}{2}}}{\cos{\frac{x}{2}} - \sin{\frac{x}{2}}} \sqrt{\operatorname{cvs}\,{x}}+c = 2\sqrt{1 + \sin{x}}+c

First, there are no corresponding 1+sinx or 1-cosx integrals listed. Second, cvs is rarely used and appears nowhere else on the page. Third, the intermediate expressions are confusing, I'm not sure if it's supposed to be a derivation. Fourth, the integrand simplifies to an expression
(|cos x/2 - sin x/2|) which can be solved using other formulas in the page. —Preceding unsigned comment added by RDBury (talk • contribs) 17:43, 16 March 2008 (UTC)

Removing

\int\sin x\,dx = -\cos x+c\,\!

It's a trivial special case of the previous integral.--RDBury (talk) 17:49, 16 March 2008 (UTC)