Is this integral using change of variables technique correct?

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WMDhamnekar
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TL;DR
https://youtu.be/TvM_SeMeg9I
Handwritten worked solution on a whiteboard converting a triple integral into spherical coordinates, with limits 0 to pi/2 for theta, 0 to 3√2 for rho, and 0 to pi/4 for phi, and the final integral in rho, phi, theta order.


Is the answer given above correct?
 

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