Question

Let R be the region enclosed by the graph of y=ln x, the line x=3, and the x-axis. (a) Fine the area of region R. (b) Find the volume of the solid generated by revolving region R about the x-axis. (c) Set up, but do not integrate, an integral expression in terms of a single variable for the volume of the solid generated by revolving region R about the line x=3. ...?

Answer 1

a.) Area of region R =
$\int\limits^3_1 {\ln{x}} \, dx =x(\ln{x}-1) \left \} {{y=3} \atop {x=1}} \right. \\=3(\ln{3}-1)-(\ln{1}-1) = 0.2958 + 1=1.2958\,square\,units$