MathDB

Today's calculation of Integral 395

Source: 1997 Tsuda Women university entrance exam

December 27, 2008

calculusintegrationgeometryconicsparabolacalculus computations

Problem Statement

3 points O(0,\ 0),\ P(a,\ a^2), Q( \minus{} b,\ b^2)\ (a > 0,\ b > 0) are on the parabpla y \equal{} x^2. Let

S_1

be the area bounded by the line

PQ

and the parabola and let

S_2

be the area of the triangle

OPQ

. Find the minimum value of

\frac {S_1}{S_2}