Find the area of the region bounded by the graphs of $y=2{{x}^{2}}+3$ and $y=-2x+7$.[3] State th

Question

Find the area of the region bounded by the graphs of $y=2{{x}^{2}}+3$ and $y=-2x+7$.[3]

State the area of the region bounded by the $2$ graphs if both graphs are translated $7$ units in the negative $y$-direction.[1]

The region $R$ is bounded by $y=2{{x}^{2}}+3$, $y=-2x+7$, the $x$-axis and the $y$-axis. Find the exact volume of the solid generated when $R$ is rotated $2\pi $ about the $y$-axis.[5]

Accepted Answer

Area $=9\text{ units}^2$ Translated area $=9\text{ units}^2$ Volume $=\dfrac{323\pi}{12}\text{ units}^3$

2024 VJC P1 Q9

2024 VJC P1 Q9

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