Region T is bounded by the graphs of and

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

Problem

Region T is bounded by the graphs of

y=\sqrt{x}

and

y=\dfrac{x}{2}+1

. The two curves intersect at

x=a

and

x=b

with

0<a<b

. Region T is revolved about the line

y=-3

to form a solid. (a) Determine the exact values of

a

and

b

. (b) For

a\le x\le b

, identify which curve forms the greater distance from the line

y=-3

and which forms the lesser distance. (c) Express the volume of the solid as the sum of two definite integrals and evaluate to find the exact volume. (d) Describe how the sign of the expression for the inner radius would change if the axis of rotation were moved to

y=5

, and explain the implication for setting up the volume integral.

Related theory

Area Between Curves
Area Applications
Volume Applications
Applications of Integration

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