Calculus of parametric equations (finding surface area)

[jrg_pz]

I was wondering what the surface area would be when the curve:

x=e^tsint,
and y=e^tcost where (t) is greater than or equal to (0) and (t) is less
or equal to pi divided by (2).
when it is revolved about
a) the x-axis
b) the y-axis (approximation with calc. (how?))

 

[amcavoy]

I was wondering what the surface area would be when the curve:

x=e^tsint,
and y=e^tcost where (t) is greater than or equal to (0) and (t) is less
or equal to pi divided by (2).
when it is revolved about
a) the x-axis
b) the y-axis (approximation with calc. (how?))

Around the x-axis you have:

$$\text{SA}_x=2\pi\int_{a}^{b}f(x)\left(\sqrt{1+f'(x)^2}\right)dx$$

...the y-axis you have:

$$\text{SA}_y=2\pi\int_{a}^{b}x\left(\sqrt{1+f'(x)^2}\right)dx$$

And I assume you can figure out what f(x) and dx are in terms of your parametric equations...