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# Polar Coordinates – Fixed integration limits – Exercise 3976

Exercise

Calculate the double integral

$$\int_0^{2\pi}d\theta\int_0^a r^2\sin^2\theta dr$$

$$\int_0^{2\pi}d\theta\int_0^a r^2\sin^2\theta dr=\frac{a^3\pi}{3}$$