Find the surface area generated by rotating the given curve about the y-axis.

x = et - t
y = 4et/2
0 ≤ t ≤ 1

I'm pretty sure the formula should be something like an integral of sqrt( (y'(t))^2 + (x'(t))^2 ) dt

But i could be wrong

Question

Find the surface area generated by rotating the given curve about the y-axis.

x = et - t
y = 4et/2
0 ≤ t ≤ 1

I'm pretty sure the formula should be something like an integral of sqrt( (y'(t))^2 + (x'(t))^2 ) dt

But i could be wrong

anonymous · Answer

$$\S=\int\limits_{a}^{b} 2pix \sqrt{(dx/dt)^2+(dy/dt)^2}dt$$

anonymous · Answer

What does the x do?

anonymous · Answer

that is the radius of the generated circular figure

anonymous · Answer

So x should be a function?

anonymous · Answer

Yea a function in respect to t

anonymous · Answer

Coool, actually i thought there was more to this one with the limits, but i guess it's just 0 to 1

anonymous · Answer

yea it is just 0 to 1 because everything is in repsect to t

anonymous · Answer

The integral looks like a good time.. lol

anonymous · Answer

um in some cases u might not be able to solve the intergral haha