MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Integrals · Applications of Integrals
Problem
Consider the region enclosed by the parabola y=x2, the x–axis, and the vertical line x=2. This region is revolved about the vertical line x=3 to create a three–dimensional solid.
Answer each part without performing any integral evaluation.
(a) State whether the resulting cross–sections perpendicular to the axis of revolution are discs or washers. Justify your choice with reference to the geometry of the region and axis.
(b) Derive expressions for both the outer and inner radius as functions of the variable used in your integral.
(c) Write a definite integral that gives the volume of the solid. Specify the limits of integration and the integrand.