Question

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?

Answer 1

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(2pi)(-sqrt(x)/e^x)*sqrt(1+(4x^2-4x+1)/(4e^(2x)*x))dx`

which I am not able to solve!!!