# Thread: Area of a surface of revolution

1. ## Area of a surface of revolution

Find the area of the surface obtained by rotating the curve about the x-axis.

$y = sin\pi x$

0 < x < 1

2. Originally Posted by FalconPUNCH!
Find the area of the surface obtained by rotating the curve about the x-axis.

$y = sin\pi x$

0 < x < 1
Where exactly are you stuck? If it's finding the integral, first make the substitution $u = \pi \cos (\pi x)$.

Now make either (not both!!) of the following substitutions

1. $u = \sinh t$ (this is the one I prefer).

2. $u = \tan t$ (more work will be required).

3. Yeah I got up to the substituting part and got confused. I haven't used the first substitution before so I don't know what to do there. I tried using tan and got lost.

4. After making the subs, did you get it down to:

$\frac{2}{\pi}\int_{-\pi}^{\pi}\sqrt{u^{2}+1}du$

Now, can you do that?.

This looks similar to a Fourier series.

5. Originally Posted by galactus
After making the subs, did you get it down to:

$\frac{2}{\pi}\int_{-\pi}^{\pi}\sqrt{u^{2}+1}du$

Now, can you do that?.

This looks similar to a Fourier series.
I finished it using table of integrals.

6. Originally Posted by FalconPUNCH!
I finished it using table of integrals.

Make it known if you'd like to see a solution using the substitution $u = \tan \theta$.