What is the surface area of the solid created by revolving f(x)=e^(2-x), x in [1, 2] around the x axis?
What is the surface area of the solid created by revolving around the x axis?
Answer & Explanation
The surface area for a revolution around the x axis is given by:
(which is basically a projection of the circumference along the function f(x) whose arc length you could have found.)
In this case, is given by:
And then we have:
First, let . Therefore, and:
where we omit the integral bounds for now. Then we can see it looks like the form , then let to get . Therefore:
And you should have written down the following integral in class:
As it turns out, , so we can remove the absolute values.
Thus, we evaluate from 1 to 2: