MathDB

ISI and CMI&#039;s newfound volume obsession

Source: CMI 2024

May 19, 2024

geometryIntegral calculuscalculus

Problem Statement

(a) Sketch qualitativly the region with maximum area such that it lies in the first quadrant and is bound by

y=x^2-x^3

and

y=kx

where

k

is a constent. The region must not have any other lines closing it. Note:

kx

lies above

x^2-x^3

(b) Find an expression for the volume of the solid obtained by spinning this region about the

y

axis.