Triple Integral between two Spheres.

[@MichaelCMartinez]

Incredible explanation! I appreciate your clarity and clean notes, as well the in-depth explanation into the integral of sin^3. Thank you!

[@aryarajmane6393]

You are an absolute legend. Please keep up the good work!

[@19917119]

Thank you for taking the time to write this. You made my day! Let me know if I can help with any math. JaberTime

[@jaisai4198]

Sir can you explain me how u took the limits for φ

[@19917119]

The Limits of Phi in Spherical Coordinates in General are from the top point on the Z-Axis all the way down to the negative Z-Axis " and that will take us from 0 to 1 Pi". Since we have two complete Spheres and not half, Theta goes from 0 to 2 Pi, and Phi goes from 0 to Pi. That is how the Spherical limits are. For Example if We are dealing with the same problem but we are asked to find the Integral between the two Spheres that is above the x-axis then Phi will go from 0 to Pi/2 only. I highley recomend that you watch the following Video that shows all the concepts of "Triple Integrals in Spherical Coordinates". It has graphs that shows and explains the limits in Spherical Coordintaes. kzbin.info/www/bejne/b5THY4Cmq8SSkNE Here is the Play List of Calculus III_Vector Calculus: kzbin.info/aero/PL3feN-fRsfCUBWwPE-mdqL5Jpdqx5Z9Ey JaberTime

[@dzungdoan6774]

thank you!

[@19917119]

You are welcome.

[@ItsNaberius]

omg thank you so much

[@19917119]

Happy to help

[@shenglanliu4197]

Hi how can i set up the triple integral in rectangular coordinates then? I know spherical coordinates is the easy way

[@19917119]

Hi, Well this is a volume between two spheres. So you can not use rectangular coordinates and that is why we need sometimes to use the Sherical coordinates. It is a sherecal shell between two shperes. How about this: Can you use rectangular coordinates if the question says: find the volume" using Triple Integration" of a sphere with radias 5 ? JaberTime