A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
Using a polar double integral, find the volume in the first octant below the surface z=xy, inside cylinder r=4cos(theta), and between the cylinders x^2 + y^2=4 and x^2 + y^2=8.
 2 years ago
Using a polar double integral, find the volume in the first octant below the surface z=xy, inside cylinder r=4cos(theta), and between the cylinders x^2 + y^2=4 and x^2 + y^2=8.

This Question is Closed

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1352751755636:dw

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2in polar the three graphs are\[r=2\]\[r=2\sqrt2\]\[r=4\cos\theta\]can you find the intersection points in terms of theta?dw:1352752221119:dw

joannaj93
 2 years ago
Best ResponseYou've already chosen the best response.0Make the equations equal to one another...

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2yes, and what do you get for theta?

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2well that's one, what angle does that correspond to? and what is the other intersection?

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2yes, 45 and 60, but you better use radians in calcdw:1352754013710:dw

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1352754159926:dw

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2so which fuunction is the outer radius and which one the inner radius for\[0\le\theta\le\frac\pi4\]?

joannaj93
 2 years ago
Best ResponseYou've already chosen the best response.0r=2 is inner and r=2sqrt2 is outer...

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2yes, good :) and for the interval\[\frac\pi4\le\theta\le\frac\pi3\]what is it?

joannaj93
 2 years ago
Best ResponseYou've already chosen the best response.0r=4cos (theta) is outer and r=2sqrt2 is inner...

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2I think you have the inner wrongdw:1352754952806:dw

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2right and what are your integrands?

joannaj93
 2 years ago
Best ResponseYou've already chosen the best response.0I'm not too sure about that

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2you are integrating xy sub in x=rcost, y=rsint

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2above t=theta in case you didn't guess also you need to use dA for polar coordinate

joannaj93
 2 years ago
Best ResponseYou've already chosen the best response.0so it'll be the double integral of r^2 cost sint...

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2that is the xy part, and what is dA in polar?

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2yes, forget that extra r and you will be sorry :P so can you write your integrals yet?

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2do you see that it will be two integrals?

joannaj93
 2 years ago
Best ResponseYou've already chosen the best response.0im getting three rs and thethas

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2there are two regions to considerdw:1352756391639:dwwhat are the bounds for r and theta on the first integral? what are they on the second? those will be the bounds of your integral.

joannaj93
 2 years ago
Best ResponseYou've already chosen the best response.0r=2 to 2√2 and t= 0 to pi/4 and r=2√2 to 4cosθ and t= 0 to pi/3

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2on the second region the lower bound on r is not 2√2 as we have already discussed, and the lower bound on theta is not 0, but the upper bound of the previous integral

joannaj93
 2 years ago
Best ResponseYou've already chosen the best response.0Sorry about that. give me a sec

joannaj93
 2 years ago
Best ResponseYou've already chosen the best response.0for the second integral: r=2 to 4cost and t= pi/4 to pi/3

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2good :) so how 'bout setting up those integrals? (two double intergals)

joannaj93
 2 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{\pi/4}\int\limits\limits_{2}^{2\sqrt{2}}r ^{2}\cos \Theta \sin \Theta r dr d \Theta \]

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2that's the first one, yes

joannaj93
 2 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{\pi/4}^{\pi/3} \int\limits_{2}^{4\cos \Theta} r2\cosΘ\sinΘrdrdΘ\]

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2yes, good :) then add them together to find the total voume happy integrating

joannaj93
 2 years ago
Best ResponseYou've already chosen the best response.0Oh, God this does not look like fun, but Thanks for the help :)

TuringTest
 2 years ago
Best ResponseYou've already chosen the best response.2It's really not that hard if you can just remember to integrate with respect to theta and r separately, but I'm still too lazy to do it. Welcome!
Ask your own question
Ask a QuestionFind 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.