Sketch, on the same diagram, the graphs of ${{x}^{2}}+{{y}^{2}}=9$ and \(y={{\mathrm{e}}^{\frac{1}

Question

Sketch, on the same diagram, the graphs of ${{x}^{2}}+{{y}^{2}}=9$ and $y={{\mathrm{e}}^{\frac{1}{4}{{x}^{2}}}}$.[2] The finite region in the first quadrant bounded by the curves ${{x}^{2}}+{{y}^{2}}=9$, $y={{\mathrm{e}}^{\frac{1}{4}{{x}^{2}}}}$, the $x$-axis, and the $y$ -axis is denoted by $R$. Shade the region $R$. [1] Find the volume of the solid of revolution formed when $R$ is rotated through $2\pi $ radians about the $x$-axis. [4]

Accepted Answer

(i) Sketch shown (ii)(a) Region $R$ shown (ii)(b) $22.7\text{ units}^3$

RI 8B Applications of Integration Tutorial Q2

RI 8B Applications of Integration Tutorial Q2

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