4. What would be the best change of variables in the double integral which yields the simplest
form?

See attached.

Write the integral in the new variables and sketch the domain of integration for the new variables. Assume that f(x) is even, i.e. that f(-t)=f(t)

5. Compute the double integral of the function (see attached) over the upper semi-circle of radius r=1. Which coordinates are more suitable for this computation?

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