A rectangle has its base on the x-axis and its upper two vertices on the semi-circle $y = \sqrt{1 - x^2}$. What is the largest area the rectangle can have?
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We have a rectangle with its base on the x-axis, so let's call the length of the base "2x" (since the rectangle is symmetric, we only need to consider half of it). The upper two vertices of the rectangle are on the semi-circle y = √(1-x^2). Let's call the Show more…
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