Let R be the region in Quadrant 1 bounded by the graphs of y=lnx and y=1.Find the exact volume of the solid generated by rotating R about the y-axis.
Thanks for help.
Let R be the region in Quadrant 1 bounded by the graphs of y=lnx and y=1.Find the exact volume of the solid generated by rotating R about the y-axis.
Thanks for help.
Simply I swap the y-axis and the x-axis so that the area is defined for $\displaystyle 0\le x \le 1$ and $\displaystyle 1\le y \le e^{x}$ and rotation is around the x axis. This conducts to use the formula...
$\displaystyle V= \pi\cdot \int_{0}^{1} f^{2}(x)\cdot dx$ (1)
... where $\displaystyle f(x)= e^{x}$, formula that leads to a more confortable integration...
Kind regards
$\displaystyle \chi$ $\displaystyle \sigma$