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Today's calculation of Integral 80

Source: 2005 Osaka University Entrance Exam

September 8, 2005

calculusintegrationalgebrafunctiondomainratiocalculus computations

Problem Statement

Let

S

be the domain surrounded by the two curves

C_1:y=ax^2,\ C_2:y=-ax^2+2abx

for constant positive numbers

a,b

. Let

V_x

be the volume of the solid formed by the revolution of

S

about the axis of

x

V_y

be the volume of the solid formed by the revolution of

S

about the axis of

y

. Find the ratio of

\frac{V_x}{V_y}