Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing

This Question is Closed

KarlaKalurky Group TitleBest ResponseYou've already chosen the best response.0
dw:1352086212618:dw
 one year ago

KarlaKalurky Group TitleBest ResponseYou've already chosen the best response.0
let u=tan theta du= sec^2 d(theta)
 one year ago

KarlaKalurky Group TitleBest ResponseYou've already chosen the best response.0
could it be: dw:1352086779624:dw ?
 one year ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.1
Are you told to do a usub of \(u=\tan(\theta)\)?
 one year ago

KarlaKalurky Group TitleBest ResponseYou've already chosen the best response.0
yes.,
 one year ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.1
Well then, you get \[\int \tan(\theta)^2\sec(\theta)^4 d\theta\]With a usub of \(u=\tan(\theta)\), we have \(du=\sec(\theta)^2d\theta\), so it seems like we get\[\int u^2\sec(\theta)^2 du\]or\[\int u^2 \frac{du^2}{d\theta}\]
 one year ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.1
However, if we start back at \(du=\sec(\theta)^2d\theta\), and take the derivative again, we get \[du^2=2\tan(\theta)\sec(\theta)^2d\theta^2.\]Honestly, I'm not sure where we're supposed to go with that usub.
 one year ago

KarlaKalurky Group TitleBest ResponseYou've already chosen the best response.0
dw:1352087930624:dw ?
 one year ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.1
What I seem to be getting, is this. I'm not quite sure what to do with it.\[\int u^2\frac{(du)^2}{d\theta}\]
 one year ago

KarlaKalurky Group TitleBest ResponseYou've already chosen the best response.0
uhm...just try to write your solution. ill appreciate it :)
 one year ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.1
Hold on a second. I think I know what you need to do. Let \(u=\tan(\theta)\). Then use the identity \(\sec(\theta)^2=\tan(\theta)^2+1\). That means we now have\[\large \int \tan(\theta)^2(\tan(\theta)^2+1)\sec(\theta)^2 d\theta\]Now you make the usub.
 one year ago

KingGeorge Group TitleBest ResponseYou've already chosen the best response.1
We get \[\large \int u^2(u^2+1) \;du=\int u^4+u^2 \;du.\] This you should be able to integrate. Then just substitute \(u=\tan(\theta)\) back in, and you're good.
 one year ago

KarlaKalurky Group TitleBest ResponseYou've already chosen the best response.0
thanks a lot!! :)
 one year ago

KarlaKalurky Group TitleBest ResponseYou've already chosen the best response.0
dw:1352125444501:dw dw:1352125609551:dw
 one year ago
See more questions >>>
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.