MHB ANSWER CHECK: Double Integral in Polar

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The discussion revolves around a double integral problem approached using polar coordinates. The original poster seeks confirmation on the correctness of their solution. Respondents affirm that the approach and answer are correct. The interaction highlights the importance of peer verification in solving complex mathematical problems. Overall, the inquiry is resolved positively with validation from the community.
Pull and Twist
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Here is the problem I am dealing with...
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And this is how I approached it. Can anyone confirm that I did it correctly and got the right answer?

View attachment 6028

Thank you.
 

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PullandTwist said:
Can anyone confirm that I did it correctly and got the right answer?
Yes, it's all good. (Yes)
 
Thank you for verifying it for me. 🙂
 
Thread 'Problem with calculating projections of curl using rotation of contour'

Thread 'Problem with calculating projections of curl using rotation of contour'

Hello! I tried to calculate projections of curl using rotation of coordinate system but I encountered with following problem. Given: ##rot_xA=\frac{\partial A_z}{\partial y}-\frac{\partial A_y}{\partial z}=0## ##rot_yA=\frac{\partial A_x}{\partial z}-\frac{\partial A_z}{\partial x}=1## ##rot_zA=\frac{\partial A_y}{\partial x}-\frac{\partial A_x}{\partial y}=0## I rotated ##yz##-plane of this coordinate system by an angle ##45## degrees about ##x##-axis and used rotation matrix to...
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