Evaluating a Triple Integral in Spherical Coordinates
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Uploader Comments (patrickJMT)
All Comments (155)
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This is a basic example, transforming triple integrals to spherical coordinates with more complex regions should have been the follow-up video.
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Can we apply Fubini's theorem for any triple integral problem involving spherical coordinates? What if you are dealing with a sphere that is not centered at the origin? My professor never introduced it, so I didn't know that you could break up the integrals like that. I have an exam tomorrow and that trick would really help me out.
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@soph6ia I think that's because it should be d phi d theta instead of d theta d phi , with the same bounds. Tell me if I am wrong...
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I think he broke up the integral like that because if you integrate sin(theta) form 0 to 2pi you will get 0, and the volume cannot be 0
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Whats the easiest way to remember or derive spherical coordinate conversions especially where grad and grad^2 are involved? Anyone got any tips?
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@soph6ia I think the relation x^2+y^2+z^2=p^2 is already accounted for in the dv formula he used (p^2*sin(phi)*dp*dphi*dtheta), so in including the function, he counted it twice and ended up with r^5/5 instead of r^3/3.
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You are essentially finding the volume of a sphere. Isn't the volume of a sphere 4/3 * pi * r^3? When r =1, V = 4/3 pi. He gets 4/5 pi. Wonder what the problem is.
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@andydrew129 When you're integrating in terms of any variable, treat the other variables like constants. So just like the (integral of 3x) = (3 * Integral of x), the same works if you take [sin(phi) * dphi * dtheta] out of the first integral (which is in terms of rho) out of that integral into the integral in terms of theta. The dtheta stays in that integral but the sin(phi)* dphi moves out into the last integral.
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omg oyu are great man i am froim india and here teacher literally teaches nothing..... my end sems starts day after tommorow and today i feel i am going to pass the!!1
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you're left handed I automatically love you. and watching your video for only a minute and I already understand more that I have been missing in my calculus class, lol
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My teacher never even told us we could break up the integral like that and multiply it out........curse that woman....
Matmo11 4 months ago 7
@Matmo11 only in certain cases
patrickJMT 4 months ago 5