Calculus 3: Triple Integrals (5 of 25) Finding the Volume of a Semi-Sphere: Spherical

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In this video I will find volume of a semi-sphere using triple integrals in the spherical coordinate system.

Next video in this series can be seen at:

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This is the first video that actually does the math and doesn't just say "oh in this case the answer is obvious" and just plug in the formula for the volume of a sphere.

lbgstzockt

when you have a final in two hours but dont know what to do

sauravshrestha

One recomendation sir, please don't keep changing the conventions for r and rho and then for phi and theta... Gets a little confusing sometimes. Great lecture by the way❤❤

joanofArc

The Thumbnail has the wrong result btw! Thank you so much for such a well made video

arushverma

WOW, Michel... WHO knew that Calculus was SO EASY !!! .. oh wait... it's Easy watching YOU do the :D ... nicely done!!

ptyptypty

thank you sir!!! this was really helpful

iqqss_

Hey, so if I want to calculate the volume of only a part of the dome? Can I just choose a different limit for Phi?

shaykreiser

Thank you so much for this Sir. You helped me again.

lordyabo

Why is θ not taken from 0 to π? I mean it doesn't matter which side the angle is taken from the x axis, ain't it? Like in the case of phi.

kanchanpathak

if you were to go for the Volume of a Total Sphere... the upper limit would be PI.. and therefore the final integration would be [ -cos(PI) - (-cos(0)] = -(-1) -(-1) = 2.. therefore 2(2(pi)/3)r^3 = (4/3)(Pi)r^3 .. voila!!... wow, MATH REALLY WORKS!! Who KNEW??? lol gee, here I am learning about Triple Integration in regards to Volume using Spherical Coordinates and TODAY is MEMORIAL DAY!! May 29th, 2017.... I guess the COOK OUT can wait...

ptyptypty

Does the order matter? Is it possible to do first phi then theta and then r for example?

gijswiersema

This may be taking things a bit further but I have questions:
1) Why can't we do this using both theta and phi going between 0 and pi?
2) Where does the function inside the integral come from?
Thanks

katiakominski

Very clear thank you sir👍👍👍 my class book wasnt clear enough !!!this is very helpful

minijginger

i'm so confused as to why we can't do phi from 0 to 2pi and theta from 0 to pi. i know the answer will be wrong, but why?

NotLegato

what happens with constants for each integral?

mateusnascimento

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