Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
joannaj93
Group Title
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
 2 years ago
joannaj93 Group Title
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
 2 years ago

This Question is Closed

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

TuringTest Group TitleBest ResponseYou've already chosen the best response.2
in 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
 2 years ago

Algebraic! Group TitleBest ResponseYou've already chosen the best response.0
1st octant...
 2 years ago

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

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

joannaj93 Group TitleBest ResponseYou've already chosen the best response.0
arccos 2^(1/2)/2
 2 years ago

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

joannaj93 Group TitleBest ResponseYou've already chosen the best response.0
45 degrees
 2 years ago

joannaj93 Group TitleBest ResponseYou've already chosen the best response.0
and 60 degrees
 2 years ago

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

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

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

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

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

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

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

joannaj93 Group TitleBest ResponseYou've already chosen the best response.0
oh, inner is r=2
 2 years ago

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

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

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

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

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

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

joannaj93 Group TitleBest ResponseYou've already chosen the best response.0
sorry, r dr dt
 2 years ago

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

joannaj93 Group TitleBest ResponseYou've already chosen the best response.0
I dont think so
 2 years ago

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

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

TuringTest Group TitleBest ResponseYou've already chosen the best response.2
there 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.
 2 years ago

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

TuringTest Group TitleBest ResponseYou've already chosen the best response.2
on 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
 2 years ago

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

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

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

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

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

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

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

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

TuringTest Group TitleBest ResponseYou've already chosen the best response.2
It'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!
 2 years 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.