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Thanks

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Which method looks correct to you?

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The second one. My question is, is there anyway that I can keep using cylindrical coordinate without changing back to cartesian coordinate and get the same solution?Which method looks correct to you?

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The second one. My question is, is there anyway that I can keep using cylindrical coordinate without changing back to cartesian coordinate and get the same solution?

You must express ##\hat{\rho}## as a function of the variable with which you are integrating. Your second method looks the only viable option to me. That was using cylindrical coordinates. Using Cartesian coordinates would entail expressing the integral in terms of the Cartesian variables ##x## and ##y##.

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