MathProblemsBank

I.1.73 Double Integrals

Condition: calculate the double integral \ (\ iint_ {d} f (x, y) d x d y \) from the function \ (f (x, y) \) in the area \ (d \) using polar coordinates. \ [\ begin {array} {l} f (x, y) = \ sqrt {\ frac {1-x^{2} -y^{2}} {1+x^{2}+y^{2}} \\ D: x^{2}+y^{2} = 1, \ quad x \ geq 0, \ quad y \ geq 0 \ end {array} \]

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.