Region $A$ is bounded by $y=4-{{\left( \ln x \right)}^{2}}$ and $y=1$. Find the volume of \(A\

Question

Region $A$ is bounded by $y=4-{{\left( \ln x \right)}^{2}}$ and $y=1$. Find the volume of $A$ rotated through $2\pi $about $x$-axis; the volume of $A$ rotated through $2\pi $ about $y$-axis; the volume of $A$ rotated through $360{}^\circ $ about the line $y=1$; the volume of $A$ rotated through $360{}^\circ $ about the line $x={{e}^{-\sqrt{3}}}$.

Accepted Answer

(i) $122$ units$^3$ (ii) $124$ units$^3$ (iii) $64.4$ units$^3$ (iv) $114$ units$^3$

Applications of Integration - Volume of Revolution about the y-axis

Applications of Integration - Volume of Revolution about the y-axis

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