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Find the area enclosed by the ellipse (...

Find the area enclosed by the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1`.

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To find the area enclosed by the ellipse given by the equation \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\), we can follow these steps: ### Step 1: Understand the Geometry of the Ellipse The ellipse is symmetric about both the x-axis and the y-axis. The semi-major axis is \(a\) along the x-axis, and the semi-minor axis is \(b\) along the y-axis. ### Step 2: Set Up the Integral for Area Calculation To find the area enclosed by the ellipse, we can calculate the area in the first quadrant and then multiply it by 4 (since the ellipse is symmetric in all four quadrants). ...
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