<p>$R$ is the finite region in the first quadrant which is bounded by the curve $\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1$ and the line $\frac{x}{a}+\frac{y}{b}=1$, where $a>b>0$.</p>
<p>Write down the definite integral representing the area of $R$ and evaluate this integral using the substitution $x=a\sin \theta$ in exact form.</p>

$R$ is the finite region in the first quadrant which is bounded by the curve $\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1$ and the line $\frac{x}{a}+\frac{y}{b}=1$, where $a>b>0$.

Write down the definite integral representing the area of $R$ and evaluate this integral using the substitution $x=a\sin \theta$ in exact form.

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International Baccalaureate Higher Level Mathematics

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Volume of Revolution Q1

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