$R$ is the region enclosed by the line $y=-5$ and the curves $y=-{{x}^{2}}+2x-5$ and \(\frac{{

Question

$R$ is the region enclosed by the line $y=-5$ and the curves $y=-{{x}^{2}}+2x-5$ and $\frac{{{x}^{2}}}{4}+\frac{{{\left( y+5 \right)}^{2}}}{16}=1$ as shown in the diagram below. Find the volume generated by region $R$ when it is rotated $2\pi $ radians about the $x$-axis. Leave your answer correct to $2$ decimal places.

Accepted Answer

$146.91$

2018 SRJC P2 Q1

2018 SRJC P2 Q1

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