Question

Find the area of the surface obtained by rotating
y = cosh x
over [−ln 2, ln 2] around the x–axis.

Answer 1

Do you know the integration surface area formula for this case?

Answer 2

It is very similar to taking the circumference of a circle with the function as your radius, and multiplying by a tiny width along the curve called ds / adding up all those little areas.

Answer 3

We generally change out ds for dx or dy using the definition given to ds:

Factoring (dx)^2 and taking the square root of both sides:
(ds)^2 = (dx)^2 + (dy)^2
(ds)^2 = (1 + (dy/dx)^2 ) (dx)^2
ds = sqrt(1 + dy/dx ^2) dx

Answer 4

This is a good resource for more information if I don't return for any responses. :)
http://tutorial.math.lamar.edu/Classes/CalcII/SurfaceArea.aspx