## Calculus 10th Edition

$\pi(24\ln{4} -\frac{27}{4})$
Setup the integration using washer method about the line y=4 $\pi \int_0^3 [(4)^2 - (4-\frac{3}{1+x})^2]dx$ $\pi \int_0^3(16-(16-\frac{24}{1+x}+\frac{9}{(1+x)^2}))dx$ $\pi \int_0^3(\frac{24}{1+x}- \frac{9}{(1+x)^2})dx$ $\pi \int_0^3 (24u^{-1} - 9u^{-2})du$, use u substitution to integrate $\pi [ 24\ln{u} +\frac{9}{u}]_1^4$ , use change of variables and evaluate the definite integral $\pi((24\ln{4} +\frac{9}{4})-(24\ln{1} +9))$ $\pi(24\ln{4} -\frac{27}{4})$