# What is the surface area of the solid created by revolving f(x)=e^(x^2+x-1)/(x+1) over x in [0,1] around the x-axis?

Jan 16, 2017

$\approx 1.45099$

#### Explanation:

The Volume of Revolution about $O x$ is given by:

$V = {\int}_{x = a}^{x = b} \setminus \pi {y}^{2} \setminus \mathrm{dx}$

So for for this problem:

$V = {\int}_{0}^{1} \setminus \pi {\left({e}^{{x}^{2} + x - 1} / \left(x + 1\right)\right)}^{2} \setminus \mathrm{dx}$

There is no elementary anti-derivative. The solution can be found numerically as $\approx 1.45099$