For a region bounded on by and with

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

For a region bounded on

[a,b]

x=f_{1}(y)

and

x=f_{2}(y)

with

f_{2}(y)\ge f_{1}(y)

, the entire region lies to the left of the vertical line

x=k

(with

k>f_{2}(y)

for all

y

). After the region is revolved about

x=k

, which of the following represents the square of the outer radius of a typical washer at height

y

? (a)

(k-f_{2}(y))^{2}

(b)

(k-f_{1}(y))^{2}

(c)

(f_{2}(y)-f_{1}(y))^{2}

(d)

\bigl(k-\tfrac{f_{1}(y)+f_{2}(y)}{2}\bigr)^{2}