Question

Find the volume of the solid obtained by rotating the region under the graph of the function f(x)=e^x about the x-axis over the interval [0,3]

Answer 1

\[V=\pi\int\limits_{0}^{3}f^2(x)dx\]

Answer 2

Alternatively, you have
\[\large V=2\pi\left(\int_0^1(3-0)\,dy+\int_1^{e^3}(3-\ln y)\,dy\right)\]