The region between curves $y= {\sqrt x}$ , $0≤x≤4,y=1,x=4$ is revolved about $y=1$. Find the volume of a generated solid.


I believe I need to find volume outlined by green, blue and dotted, black line (like on the graph).

$V = \pi $$\int_1^4 ({\sqrt x})^2 \,dx$. Is it correct approach or should I calculate $\pi $$\int_0^4 ({\sqrt x})^2 \,dx$ instead or maybe there is different approach.


Hint: You have to calculate $$\pi\int_1^4(\sqrt{x}-1)^2dx$$ which is the volume of the curve $\sqrt{x}-1$ revolved around $y=0$ instead.


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