Consider the region bounded on the left by the parabola

MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Consider the region

S

bounded on the left by the parabola

x=(y-1)^{2}

, on the right by the line

x=y+2

, and between the horizontal lines

y=1

and

y=3

. Squares are erected on

S

so that each square has one side lying in

S

and its interior perpendicular to the y-axis. (a) Find the y-coordinates of the points where the two bounding curves of

S

intersect. (b) Compute the exact volume of the solid whose base is

S