Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
stamp
Group Title
[CALCULUS III—DOUBLE INTEGRALS] Evaluate by converting to polar coordinates. (figure inside)
 one year ago
 one year ago
stamp Group Title
[CALCULUS III—DOUBLE INTEGRALS] Evaluate by converting to polar coordinates. (figure inside)
 one year ago
 one year ago

This Question is Closed

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

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

zepdrix Group TitleBest ResponseYou've already chosen the best response.2
Let'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
 one year ago

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

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

stamp Group TitleBest ResponseYou've already chosen the best response.0
Hey 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.
 one year ago

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

zepdrix Group TitleBest ResponseYou've already chosen the best response.2
Changing 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.\[\large dx\;dy \qquad \rightarrow \qquad r\;dr\;d\theta\]
 one year ago

zepdrix Group TitleBest ResponseYou've already chosen the best response.2
Haha 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
 one year ago

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

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