Beregn volumet over z=x2+y2z=x^2+y^2z=x2+y2 og under z=4z=4z=4.
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V=2π∫02(4−r2)r dr=2π∫02(4r−r3)dr=2π[2r2−r44]02=2π(8−4)=8πV=2\pi\int_0^2(4-r^2)r\,dr=2\pi\int_0^2(4r-r^3)dr=2\pi[2r^2-\tfrac{r^4}{4}]_0^2=2\pi(8-4)=8\piV=2π∫02(4−r2)rdr=2π∫02(4r−r3)dr=2π[2r2−4r4]02=2π(8−4)=8π.
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