<p>The curves ${{C}_{1}}$ and ${{C}_{2}}$ have equations $y=\sqrt{15x+4}$ and $y={{x}^{2}}-2$ respectively. The region $R$ is bounded by the $y$-axis, ${{C}_{1}}$ and ${{C}_{2}}$.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Show algebraically that the point with coordinates $\left( 3,7 \right)$ is the only point of intersection between ${{C}_{1}}$ and ${{C}_{2}}$.</div><p style="text-align: right;">[3]</p></li><li><div class="list-item-paragraph">Without the use of a graphing calculator, find the exact area of $R$.</div><p style="text-align: right;">[4]</p></li><li><div class="list-item-paragraph">Find the volume of revolution when $R$ is rotated $2\pi $ radians about the $y$-axis.</div><p style="text-align: right;">[3]</p></li></ol>

The curves ${{C}_{1}}$ and ${{C}_{2}}$ have equations $y=\sqrt{15x+4}$ and $y={{x}^{2}}-2$ respectively. The region $R$ is bounded by the $y$-axis, ${{C}_{1}}$ and ${{C}_{2}}$.

Show algebraically that the point with coordinates $\left( 3,7 \right)$ is the only point of intersection between ${{C}_{1}}$ and ${{C}_{2}}$.

Without the use of a graphing calculator, find the exact area of $R$.

Find the volume of revolution when $R$ is rotated $2\pi $ radians about the $y$-axis.

2023 DHS Promo Q10

2023 DHS Promo Q10

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