MathProblemsBank

i.1.73 Double integrals

Condition: Calculate the double integral \( \iint_{D} f(x, y) d x d y \) of the function \( f(x, y) \) over the domain \( D \), 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 iterated integrals over various areas of integration, conversion from Cartesian to polar coordinates, calculation of the Jacobian, changing the limits of integration, transformation of variables in the integral.

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