The upper half of the ellipse centered at the origin with axes of length \( 2 a \) and \( 2 b \) is described by \( y=\frac{b}{a} \sqrt{a^{2}-x^{2}} \) as shown in the figure. Find the area of the ellipse in terms of a and \( b \). The area of the ellipse is . (Type an exact answer in terms of \( \pi \).) \( \cdots \)
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First, we need to find the area of the upper half of the ellipse. To do this, we can integrate the given equation with respect to x from -a to a: Area_upper_half = ∫[ (b/a) * sqrt(a^2 - x^2) ] dx from -a to a Show more…
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The upper half of the ellipse centered at the origin with axes of length $2 a$ and $2 b$ is described by $y=\frac{b}{a} \sqrt{a^{2}-x^{2}}(\text { see figure }) .$ Find the area of the ellipse in terms of $a$ and $b$
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Area of an ellipse The upper half of the ellipse centered at the origin with axes of length $2 a$ and $2 b$ is described by $y=\frac{b}{a} \sqrt{a^{2}-x^{2}}$ (see figure). Find the area of the ellipse in terms of $a$ and $b.$ (FIGURE CAN'T COPY)
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