It is given that $O$ is the origin and $A$ is the point on the curve \(y=x{{\mathrm{e}}^{x}

Question

It is given that $O$ is the origin and $A$ is the point on the curve $y=x{{\mathrm{e}}^{x}}$ where $x=3$. The region bounded by the curve $y=x{{\mathrm{e}}^{x}}$and the line $OA$ is rotated through ${{360}^{\circ }}$ about the $x$-axis. Find the exact volume of the solid formed.[7]

Accepted Answer

$\frac{\pi}{4}(23e^6 + 1)$ units$^3$

2021 YIJC P1 Q5

2021 YIJC P1 Q5

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