Consider a solid whose rectangular cross sections are taken perpendicular to the…

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Consider a solid whose rectangular cross sections are taken perpendicular to the

x

-axis over the interval

[a,b]

. Each cross section has height

k

times its base width, where

k>0

is constant and the width at

x

f(x)-g(x)

. Explain how the value of

k

affects the volume of the solid when the region between

y=f(x)

and

y=g(x)

remains fixed.