Question

Find the volume of the solid of revolution formed by rotating about the x--axis the region bounded by the given curves.

Answer 1

Answer:

$\frac{\pi}{2} (e^4-1)$

Step-by-step explanation:

We are given: $f(x)=e^x$

The volume will be calculated via the integral as follows,

$V=\pi\int\limits^2_0(e^x)^2dx=\pi\int\limits^2_0e^{2x}dx=\pi \frac{e^{2x}}{2} |^2_0 = \frac{\pi}{2} (e^4-e^0)=\frac{\pi}{2} (e^4-1)$