Find the volume of the solid formed when $y = \sqrt{x}$ between $y = 1$ and $y = 4$ is revolve

Question

Find the volume of the solid formed when $y = \sqrt{x}$ between $y = 1$ and $y = 4$ is revolved about the $y$-axis by $2\pi$ ; $y = \ln x$ between $y = 0$ and $y = 2$ is revolved about the $y$-axis by $2\pi$ .

Accepted Answer

(i) $\frac{1023\pi}{5}$ cubic units. (ii) $\frac\pi2(\mathrm e^4-1)$ cubic units.

Volume of revolution about y-axis

Volume of revolution about y-axis

Solution:

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