# What is the surface area of the solid created by revolving f(x)=-sqrtx/e^x over x in [0,1] around the x-axis?

Jan 22, 2018

I got as far as the definite integral but then I got stuck at the solution of the integral....probably there is a mistake or there is an easier way...

#### Explanation:

I considered the function and the rotation:

then I used the standard technique:

giving the expression of the surface area $S$ as:

$S = {\int}_{0}^{1} \left(2 \pi\right) \left(- \frac{\sqrt{x}}{e} ^ x\right) \cdot \sqrt{1 + \frac{4 {x}^{2} - 4 x + 1}{4 {e}^{2 x} \cdot x}} \mathrm{dx}$

which I am not able to solve!!!