How Do You Compute Arc Length and Surface Area for the Exponential Curve e^x?

[froogle30]

C: y=f(x)=e^x, where x is all real numbers.
Compute the arc-length function S for C relative to C's y-intercept
Computer the area S for the surface generated by revolving the curve C*:y=f(x)=e&x, where x is [0,a] and a is a positive constant, about the x-axis

I've been trying this problem for 2 weeks and have gotten stuck. I usually don't ask for help because I figure that help doesn't get me anywhere and that I prefer to do everything on my own, but this problem is due after spring break, which is on Monday. I've done this problem to the point where my head literally feels like exploding. Please..someone help.

The answer I ended up with ln |csc theta - cotangent theta|. Thanks

 

[tiny-tim]

Welcome to PF!

Hi froogle30! Welcome to PF!

(have a theta: θ and a pi: π and try using the X² tag just above the Reply box )

C: y=f(x)=e^x, where x is all real numbers.
Compute the arc-length function S for C relative to C's y-intercept
Computer the area S for the surface generated by revolving the curve C*:y=f(x)=e&x, where x is [0,a] and a is a positive constant, about the x-axis
…
The answer I ended up with ln |csc theta - cotangent theta|.

Show us how you got ln(cscθ - cotθ), and then we can see what went wrong, and we'll know how to help