A region in the first quadrant is enclosed by the graphs of and for
MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Integrals · Applications of Integrals
Problem
A region in the first quadrant is enclosed by the graphs of y=x and y=x for 0≤x≤1. The region is revolved about the x-axis to generate a solid of revolution.
(a) For an arbitrary value of x in the interval [0,1], describe which of the two given functions determines the distance from the x-axis to the outer edge of a typical circular cross-section and which determines the distance to the inner edge. Justify your answer using properties of the two graphs.
(b) Explain why the limits of integration for any integral expression representing the volume of the solid are x=0 and x=1.
(c) Write, but do not evaluate, a definite integral whose value is the exact volume of the solid generated by the rotation described above.