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Q53Section C (Section C)53 of 60

Lower angle limit from a polar double integral

The value of the real number mm in the following equation

∫01∫x2−x2(x2+y2)dy dx=∫mππ/2∫02r3 dr dθ\int_0^1\int_x^{\sqrt{2-x^2}}\left(x^2+y^2\right)dy\,dx=\int_{m\pi}^{\pi/2}\int_0^{\sqrt2}r^3\,dr\,d\theta

is ________________________

Numerical answer: type the number (no options).

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