What coordinate system is suggested to be used when seeing the integrand (x^{2}+y^{2})^{5/2}, cylindrical or Cartesian?

remolatg 2021-08-03 Answered
a) What coordinate system is suggested to be used when seeing the integrand \(\displaystyle{\left({x}^{{{2}}}+{y}^{{{2}}}\right)}^{{\frac{{5}}{{2}}}}\), cylindrical or Cartesian?
b) List the conversion factors for rectangular to cylindrical coordinate systems.

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Expert Answer

un4t5o4v
Answered 2021-08-04 Author has 5066 answers
Step 1
We determine which coordinate system is used
Step 2
a) \(\displaystyle{\left({x}^{{{2}}}+{y}^{{{2}}}\right)}^{{\frac{{5}}{{2}}}}\)
cylindrical
b) we know that
\(\displaystyle{x}^{{{2}}}+{y}^{{{2}}}=\gamma^{{{2}}}\)
\(\displaystyle{\left({x}^{{{2}}}+{y}^{{{2}}}\right)}^{{\frac{{5}}{{2}}}}={\left(\gamma^{{{2}}}\right)}^{{\frac{{5}}{{2}}}}\)
\(\displaystyle=\gamma^{{{5}}}\)
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