Today's calculation of Integral 280
Source: 1982 Kobe University entrance exam
January 23, 2008
calculusintegrationanalytic geometrytrigonometrygeometrylogarithmscalculus computations
Problem Statement
Let be the coordinates of curves x^2 \plus{} y^2 \equal{} 1,\ y\geq 0 and y \equal{} \frac {1}{4x}.
(1) Find such that \cos \frac {\alpha}{2} \equal{} p,\ \cos \frac {\beta }{2} \equal{} q\ (0 < \alpha < \pi ,\ 0 < \beta < \pi).
(2) Find the area bounded by the curves.