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Today's calculation of Integral 895

Source: 2013 Yokohama City University entrance exam/Medicine

October 5, 2013
calculusintegrationanalytic geometryconicsparabolageometrycalculus computations

Problem Statement

In the coordinate plane, suppose that the parabola C:y=−p2x2+q (p>0, q>0)C: y=-\frac{p}{2}x^2+q\ (p>0,\ q>0) touches the circle with radius 1 centered on the origin at distinct two points. Find the minimum area of the figure enclosed by the part of y≥0y\geq 0 of CC and the xx-axis.
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