MathDB

Today's calculation of Integral 267

Source: 1983 Tokyo University entrance exam/Science

January 17, 2008

calculusintegrationconicsparabolacalculus computations

Problem Statement

Let

K

be the curved surface obtained by rotating the parabola y \equal{} \frac {3}{4} \minus{} x^2 about the

y

-axis.Cut

K

by the plane

H

passing through the origin and forming angle

45^\circ

for the axis. Find the volume of the solid surrounded by

K

and

H.

Note that you are not allowed to use Double Integral for the problem.