A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
Help with integrals
anonymous
 5 years ago
Help with integrals

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what do you need help with?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{}^{}\frac{dx}{\sin^2x}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I got stuck here :\[2\int\limits_{}^{}\frac{dx}{1\cos(2x)}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hold on let me write it out ok?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but btw the 1cos(2x) use trig identitites.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits 1\div \sin x ^{2} dx = x / sinx ^{2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.01/tan x sorry wrong answer.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It's normally assumed from the fact \[\frac{\mathbb{d}}{\mathbb{d}x} \cot x = cosec^2x\] .... but if you REALLY want to prove it, try the sub \[t = \tan \frac{x}{2} \] Haven't tried it, but it almost always works. May be some easy way I'm missing.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Note, proving the differentiation version, if you deem that sufficient, is far easier. But if you did not know the result, the sub I guess would be OK.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0moolean, i'd stick with what hes saying, i think he understand integrals better then i do. im nto perfect at it yet, i was just trying to help, but he seems to rlly know what he's talking about.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\text{Let } t = \frac{\tan{x}}{2} \implies \frac{\mathbb{d}x}{\mathbb{d}t} = \frac{2}{1+t^2} \] It quickly follows that: \[\sin x = \frac{2t}{1+t^2}\] \[\int \frac{1}{sin^2x} \mathbb{d}x = \int \left(\frac{1+t^2}{2t}\right)^2\cdot \frac{2}{1+t^2} \mathbb{d}t = \int \left(\frac{1+t^2}{2t^2}\right)\cdot \mathbb{d}t \] \[\int \left(\frac{1+t^2}{2t^2}\right)^2\cdot \mathbb{d}t = \frac{t^2  1}{2t} \] Which, from double angle formulae, is equal to the required result.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It did work, after all :D

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0gj Newton :P that's impressive.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Thanks  I needed to practice it anyway. NOTE there should be no squared on the fraction on the last line. some dodgy copy/pasting from above there :(

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0THAT;S A GREAT HELP. THANKS!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ugh, the sub is \[ t = \tan \frac{x}{2} \] So many typos :/ But you're welcome.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0geez i should say thank you too, u taught me something and i was only trying to help :P
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.