You are Here: Home

# Integration of cosec^2x

Announcements Posted on
International student planning UK study in 2016? Take our short survey and we’ll send you a £5 Amazon voucher 03-05-2016
Talking about ISA/EMPA specifics is against our guidelines - read more here 28-04-2016
1. Hi i no from formula sheets that the integral of cosec^2x equals -cotx but i still cant work out how to prove this integral.

so far iv tried a few different things

1. i no that cosec^2=1/sin^2x but this doesnt help much

2. cosec^2x=cot^2x + 1, again... couldn't get much further with that

any help would be greatly appreciated
thanks
2. differentiate -cotx and voila!
3. thanx that was really helpful, do u no a method of integrating it without using differentiation i.e. going straight from cosec^2x to -cotx
4. (Original post by e-unit)
nice one.
5. (Original post by Mattios88)
Hi i no from formula sheets that the integral of cosec^2x equals -cotx but i still cant work out how to prove this integral.

so far iv tried a few different things

1. i no that cosec^2=1/sin^2x but this doesnt help much

2. cosec^2x=cot^2x + 1, again... couldn't get much further with that

any help would be greatly appreciated
thanks
Hey, I thought I'd help you out as I've just done this problem myself. Use translation: as sin(x)=cos((pi/2)-x) cosec(x)=sec((pi/2)-x) so cosec^2(x)=sec^2((pi/2)-x)
this is easily integratable as I(sec^2(x))=tanx:
I(sec^2((pi/2)-x))=-tan(pi/2-x)+k = -cot(x)+k
6. (Original post by korobeiniki)
Hey, I thought I'd help you out as I've just done this problem myself. Use translation: as sin(x)=cos((pi/2)-x) cosec(x)=sec((pi/2)-x) so cosec^2(x)=sec^2((pi/2)-x)
this is easily integratable as I(sec^2(x))=tanx:
I(sec^2((pi/2)-x))=-tan(pi/2-x)+k = -cot(x)+k
I doubt that dude will ever come back on here again lol.

BUT I might as well ask you to note that his question asked how to get the integral of without having prior knowledge that -cot(x) differentiates to it. In your explanation, you use a change of trig functions which is fine but the one part that you haven't explained is how . Of course, we know that if we differentiate tan(x), we get sec^2(x) but this does not solve his original question.

If you want to look at how you could, have a look at t-substitutions.
7. Awesome! This helps a lot. Thanks

## Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
2. this can't be left blank
3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
1. Oops, you need to agree to our Ts&Cs to register

Updated: November 11, 2014
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Today on TSR

How did it go?

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read here first

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams