What is the surface area when a curve is rotated about the x-axis?

[californicate]

Homework Statement

Obtain the surface area when the curve y=e^x, 0≤x≤1, is rotated about the x-axis

Homework Equations

Surface Area = 2∏_a∫^b x√(1+(dy/dx)²)dx

The Attempt at a Solution

I started with the the equation, Surface Area = 2∏₀∫¹ x√(1+e^2x)dx. However, whichever way I try to integrate I end up getting stuck. By substitution, Nothing ends up working so that the integral becomes simpler, much less only according to one variable. By parts, I just end up with messier and messier integrals. How should I approach this problem?

Thanks!

 

[Saitama]

Homework Statement

Obtain the surface area when the curve y=e^x, 0≤x≤1, is rotated about the x-axis

Homework Equations

Surface Area = 2∏_a∫^b x√(1+(dy/dx)²)dx

The Attempt at a Solution

I started with the the equation, Surface Area = 2∏₀∫¹ x√(1+e^2x)dx. However, whichever way I try to integrate I end up getting stuck. By substitution, Nothing ends up working so that the integral becomes simpler, much less only according to one variable. By parts, I just end up with messier and messier integrals. How should I approach this problem?

Thanks!

Hi californicate! Welcome to PF!

Your relevant equation doesn't look right to me. :)

 

[californicate]

So should the x inside the integral be replaced with an f(x)? That's the equation the prof gave in class, however in examples he switched back and forth between using f(x) and x. I'll ask about it next class.

Thanks!

 

[Saitama]

So should the x inside the integral be replaced with an f(x)?

Yes!

http://tutorial.math.lamar.edu/Classes/CalcII/SurfaceArea.aspx