A community for students.
Here's the question you clicked on:
 0 viewing
 one year ago
[CALCULUS III—DOUBLE INTEGRALS] Evaluate by converting to polar coordinates. (figure inside)
 one year ago
[CALCULUS III—DOUBLE INTEGRALS] Evaluate by converting to polar coordinates. (figure inside)

This Question is Closed

stamp
 one year ago
Best ResponseYou've already chosen the best response.0\[\int_0^3\int_0^{\sqrt{9x^2}}(x^2+y^2)^{3/2}\ dydx\]

stamp
 one year ago
Best ResponseYou've already chosen the best response.0notes — http://tutorial.math.lamar.edu/Classes/CalcIII/DIPolarCoords.aspx

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Let's start by drawing the region.\[\large 0 \le y \le \sqrt{9x^2}\]Here are the boundaries on y, it appears to be the upper half of a circle, with radius 3.dw:1363217680487:dw

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2How bout the boundaries on x?\[\large 0 \le x \le 3\]This is telling us that our region is only the first quadrant.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2dw:1363217804038:dwThis is how our boundaries would change in polar.

stamp
 one year ago
Best ResponseYou've already chosen the best response.0Hey I appreciate your help. Keep posting guidelines, I am currently finishing up at work but when I get home I will be looking at this again and begin solving.

stamp
 one year ago
Best ResponseYou've already chosen the best response.0If you do decide to post a lot, leave the answer and final evaluations to me ;)

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Changing to polar, we let \(\large x=r\cos\theta\) and \(\large y=r\sin\theta\) and simplify our integral down. An important thing to remember, is that when we change the `differentials`, a factor of \(\large r\) will pop out as well.\[\large dx\;dy \qquad \rightarrow \qquad r\;dr\;d\theta\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Haha XD I prolly won't post the final answer, just some steps :D They frown on that stuff here.. If I don't let you do some of the work, heh

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2So I think this is how our integral would change. \[\large \int\limits_{\theta=0}^{\pi/2}\quad \int\limits_{r=0}^{3} \left((r \cos \theta)^2+(r \sin \theta)^2 \right)^{3/2}\left(r \;dr\;d \theta\right)\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Lemme know if you have trouble solving that. Don't forget your important trig identity, \(\large \cos^2x+\sin^2x=1\)
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.