# (integral) calculus questions **URL:** \ **Category:** Factual Questions\ **Created:** [February 11, 2004, 8:11am UTC](https://boards.straightdope.com/t/integral-calculus-questions/228624 "2004-02-11T08:11:30Z")\ **Posts on this page:** 4\ **Page:** 1
**Author:** ![Mog16](https://avatars.discourse-cdn.com/v4/letter/m/4da419/32.png) [@Mog16](https://boards.straightdope.com/u/Mog16)\ **Post date:** [February 11, 2004, 8:11am UTC](https://boards.straightdope.com/t/integral-calculus-questions/228624/1 "2004-02-11T08:11:30Z")
Hi, I’m currently taking MTH 252 (integral calculus) at my university and I am having an enormous amount of trouble understanding trigonometric integrals and trigonometric substitution. I was wondering if anyone on here could lend a hand or point me in the direction to a webpage that can assist me? I’ve done a bit of searching for websites on this topic but what I have found is in heavy ‘mathspeak’ and is even more confusing to me. ---
**Author:** ![Angua](https://avatars.discourse-cdn.com/v4/letter/a/8baadc/32.png) [@Angua](https://boards.straightdope.com/u/Angua)\ **Post date:** [February 11, 2004, 10:59am UTC](https://boards.straightdope.com/t/integral-calculus-questions/228624/2 "2004-02-11T10:59:01Z")
OK - I TA such a class, so I _should_ be able to help. I presume that you’re au fait with the standard trig identities? The aim of trigonometric substitution is to convert an expression that would be horrendous to integrate otherwise into something relatively trivial. There’s no hard and fast rule as to what substitution to use where - that comes with practice. But, knowing the derivatives of sin(x), cos(x) and tan(x), is a first step. Secondly, recognising various patterns is useful. Say if you have to evaluate the integral of (1-x^2)^(-0.5), then recognising that 1-x^2 yields (cos(u))^2, if we make the substitution x=sin(u), makes the integral exceptionally easy, since dx/du is simply cos(u), and terms cancel down, and we end up simply integrating a constant. So, that’s substitution - does that make sense? As for trigonometric integration, which bits in particular are you having problems with? ---
**Author:** ![ccwaterback](https://avatars.discourse-cdn.com/v4/letter/c/df705f/32.png) [@ccwaterback](https://boards.straightdope.com/u/ccwaterback)\ **Post date:** [February 11, 2004, 1:21pm UTC](https://boards.straightdope.com/t/integral-calculus-questions/228624/3 "2004-02-11T13:21:30Z")
Here are some websites: [http://www.math2.org/math/trig/identities.htm](http://www.math2.org/math/trig/identities.htm) > **[Trigonometric substitution](https://en.wikipedia.org/wiki/Trigonometric_substitution)** > > In mathematics, trigonometric substitution is the substitution of trigonometric functions for other expressions. In calculus, trigonometric substitution is a technique for evaluating integrals. Moreover, one may use the trigonometric identities to simplify certain integrals containing radical expressions. Like other methods of integration by substitution, when evaluating a definite integral, it may be simpler to completely deduce the antiderivative before applying the boundaries of integrat Let > ... [http://archives.math.utk.edu/visual.calculus/4/substitutions.3/index.html](http://archives.math.utk.edu/visual.calculus/4/substitutions.3/index.html) [http://www.math.hmc.edu/calculus/tutorials/trig\_substitution/](http://www.math.hmc.edu/calculus/tutorials/trig_substitution/) [http://www.maths.abdn.ac.uk/~igc/tch/ma1002/int/node37.html](http://www.maths.abdn.ac.uk/~igc/tch/ma1002/int/node37.html) ---
**Author:** ![Mog16](https://avatars.discourse-cdn.com/v4/letter/m/4da419/32.png) [@Mog16](https://boards.straightdope.com/u/Mog16)\ **Post date:** [February 12, 2004, 8:47am UTC](https://boards.straightdope.com/t/integral-calculus-questions/228624/4 "2004-02-12T08:47:10Z")
Thank you so much for the help, the websites were a great help.