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**Can't figure out my mistake in calculating volume**

I'm trying to calculate the volume of {(x,y,z)|[itex]x^2+(y-1)^2<1[/itex], [itex]0<z<\sqrt{4-x^2-y^2}[/itex]}:

[tex]\int_0^{\pi}d\theta \int_0^{2sin(\theta)}\sqrt{4-r^2}rdr=\frac {-1}{3}\int_0^\pi ((4-4sin^2\theta)^{3/2}-8)d\theta=\frac{-8}{3}(\int_0^\pi (1-sin^2\theta)\sqrt{1-sin^2\theta}d\theta-\pi)=\frac{-8}{3}(\int_{sin(0)}^{sin(\pi)} (1-u^2)du-\pi)=\frac{8\pi}{3}[/tex]

However on Wolfram Alpha I get different answer for the same integral.

What I'm doing wrong?

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