For , let denote the region bounded by the graph of , the –axis, and the vertical…

MATHEMATICS · Single correct · CBSE · Mathematics · Integrals · Integrals

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)