MathDB

Today's calculation of Integral 291

Source: 2008 Sophia University entrance exam/Psychology

February 7, 2008

calculusintegrationconicsparabolaanalytic geometrygraphing linesslope

Problem Statement

Consider the parabola C: y \equal{} x^2 in the x \minus{} y plane. Let

l_1

be the tangent line of

C

with slope

\sqrt {3}

and

l_2

be the tangent line of

C

with negative slope which makes angle

45^\circ

with

l_1

. Find the area bounded by

C,\ l_1

and

l_2