Question about volume integral

Question

The question: Find the volume of the solid obtained by rotating the region below the graph of the function $f (x) = e ^x $ on the x axis in the interval from 0 to 5

I find: 34597.5

But I believe I did it wrong.

Answer 1

You are correct.

The volume for the solid of revolution for a curve determined by the curve $f(x)$ rotated around the $x$-axis on an interval $[a,b]$ is $$V=\int_{a}^{b} \pi (f(x))^{2}dx$$

So we have $$V=\pi\int_{0}^{5}e^{2x}dx=\frac{\pi}{2}(e^{10}-1) \space(\approx 34597.5207664)$$