Let be a non-negative continuous function on

MATHEMATICS · Subjective · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Let

f

be a non-negative continuous function on

[a,b]

, and let

c>0

. The region under

y=f(x)

[a,b]

is revolved about the

x

-axis, producing a volume

V

. The region under

y=f(x)+c

on the same interval is then revolved about the

x

-axis. Express the new volume

V_{c}

in terms of

V

c

, and a definite integral involving

f