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Today's calculation of Integral 740

Source: 2011 Nagoya Institute of Technology entrance exam

July 5, 2011
calculusintegrationgeometryderivativecalculus computations

Problem Statement

Let rr be a positive constant. If 2 curves C1:y=2x2x2+1, C2:y=r2−x2C_1: y=\frac{2x^2}{x^2+1},\ C_2: y=\sqrt{r^2-x^2} have each tangent line at their point of intersection and at which their tangent lines are perpendicular each other, then find the area of the figure bounded by C1, C2C_1,\ C_2.
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