Mathematics

Mathematics

Problem

For

k>0

, let

R_k

denote the region bounded by the graph of

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

, the

x

–axis, and the vertical lines

x=0

and

x=2

. When

R_k

is revolved about the

y

–axis, the resulting solid has volume

12\pi

. Determine the value of

k

. a)

\displaystyle\frac{6}{2-\ln 3}

b)

\displaystyle\frac{6}{2+\ln 3}

c)

\displaystyle\frac{12}{2-\ln 3}

d)

\displaystyle 6\,(2-\ln 3)

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