- #1
yUNeeC
- 34
- 0
Hey guyzerz,
I'm reviewing for an upcoming Calc. III test and have come across a review problem that is giving me fits:
Evaluate the integral where E lies between the spheres p = 3 and p = 6 and above the cone phi = pi/4.
The integral is TRIPLEINT[xyz]dV
So basically, after converting to spherical coordinates, I get to where the integral (before any integration) looks like this:
(p^5)(sin^3(phi)cos(phi))(sin(theta)cos(theta))
I can split these up into:
INT[p^5] from p=6 to p=3
INT[sin^3(phi)cos(phi)] from phi = pi/4 to phi = 0
INT[sin(theta)cos(theta)] from 2pi to 0pi
The first two of these integrals are easy as pie. But on the third one, I get the integral to equal (after integration) 0.5(sin^2(theta)) from 2pi to 0...which gives me an answer of 0. This also equals zero if you integrate via u-substitution the other way around. I've tried integrating from pi/4 to 0 and multiplying the result by 8 (=2) and this doesn't work either. I really feel like I need to get my answer in terms of pi to account for the spherical nature of the problem, but I'm at a loss as to how to go about doing this.
Any help? :(
Gracias for tu time-o
PS: Yes I left off the dpdthetadphi stuff because it looked like i passed out on my keyboard.
I'm reviewing for an upcoming Calc. III test and have come across a review problem that is giving me fits:
Evaluate the integral where E lies between the spheres p = 3 and p = 6 and above the cone phi = pi/4.
The integral is TRIPLEINT[xyz]dV
So basically, after converting to spherical coordinates, I get to where the integral (before any integration) looks like this:
(p^5)(sin^3(phi)cos(phi))(sin(theta)cos(theta))
I can split these up into:
INT[p^5] from p=6 to p=3
INT[sin^3(phi)cos(phi)] from phi = pi/4 to phi = 0
INT[sin(theta)cos(theta)] from 2pi to 0pi
The first two of these integrals are easy as pie. But on the third one, I get the integral to equal (after integration) 0.5(sin^2(theta)) from 2pi to 0...which gives me an answer of 0. This also equals zero if you integrate via u-substitution the other way around. I've tried integrating from pi/4 to 0 and multiplying the result by 8 (=2) and this doesn't work either. I really feel like I need to get my answer in terms of pi to account for the spherical nature of the problem, but I'm at a loss as to how to go about doing this.
Any help? :(
Gracias for tu time-o
PS: Yes I left off the dpdthetadphi stuff because it looked like i passed out on my keyboard.