Calculus 3 Quiz
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MULTIPLE INTEGRALS
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A double integral in Cartesian coordinates has the form ∫0a∫0a2−x2g(x2+y2) dy dx\int_0^a \int_0^{\sqrt{a^2-x^2}} g(x^2+y^2) \, dy \, dx where a>0a > 0. After converting to polar coordinates and evaluating, the result is π2∫0ar⋅g(r2) dr\frac{\pi}{2}\int_0^a r \cdot g(r^2) \, dr. What relationship must hold between the original integral and the converted form?
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