MathProblemsBank

I.1.50 Double Integrals

Condition: calculate the double integral in the area \ (d: \) \ [\ iint_ {d} \ frac {\ sin \ sqrt {x^{2}+y^{2}} {\ sqrt {x^{2}+y^{2}} D X D Y \] where \ (D: x^{2}+y^{2} = \ frac {\ pi^{2}} {9}, x^{2}+y^{2} = \ pi^{2} \).

Double and itieded integrals over Various Areas of Integration, Conversion from Cartesian to Polar Coordinates, Calculation of the Jacobian, Changing the Integration, Transformation of Variables in the Integral.