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Evaluate [tex]\int\int\int y dV[/tex] where the solid generated lies between the cylinders x

I wrote out the integral [tex]\int\int r*r sin \theta dz dr d\theta[/tex] and z is integrated from x+2 to 0, r integrated from 2 to 1 and [tex]\theta[/tex] from [tex]2\pi[/tex] to 0. But I ended up with [tex]\frac{-7}{3}(x+2)cos(2\pi - 0)[/tex] which gives me 0?? I tried visualizing the volume generated and its like a donut with the top cut away at an angle. So how is the volume 0? Did I do something wrong?

^{2}+y^{2}=1 and x^{2}+y^{2}=4, above the xy-plane and below the plane z=x+2.I wrote out the integral [tex]\int\int r*r sin \theta dz dr d\theta[/tex] and z is integrated from x+2 to 0, r integrated from 2 to 1 and [tex]\theta[/tex] from [tex]2\pi[/tex] to 0. But I ended up with [tex]\frac{-7}{3}(x+2)cos(2\pi - 0)[/tex] which gives me 0?? I tried visualizing the volume generated and its like a donut with the top cut away at an angle. So how is the volume 0? Did I do something wrong?

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