Solve Integration: 4π∫x√(x2+2x+1)/4x

[elitespart]

The loop 9y^2=x(3-x)^2 is revolved about the y-axis. Find the area of the surface generated this way.

I just need help with integration:

4\pi\int x\sqrt{\frac{x^{2}+2x+1}{4x}}

I know I can pull out the 4 but after that I'm lost. Any suggestions?

 

[Dick]

x^2+2*x+1=(x+1)^2. There's another thing you can pull out.

 

[elitespart]

oh sweet. Thanks. oh if anyone has time to check could you please let me know if I set up the integral properly?

 

[Dick]

You know there is something special about problems like surface area and arc length? With that square root in them, you can almost never do them exactly. You have to set up a problem carefully to get it to have an exact solution. Since yours cracked so easily, I'm going to guess it's correct, just based on probability. But, sure, I'll check it.

 

[elitespart]

You know there is something special about problems like surface area and arc length? With that square root in them, you can almost never do them exactly. You have to set up a problem carefully to get it to have an exact solution. Since yours cracked so easily, I'm going to guess it's correct, just based on probability. But, sure, I'll check it.

thanks. and I forgot to add that it's from 0 to 3. and you're right - I ended up with 60.9422...

 

[Dick]

It looks pretty good as far as the integral goes. Why do you have 4pi instead of 2pi. I might just be getting tired.

 

[elitespart]

It looks pretty good as far as the integral goes. Why do you have 4pi instead of 2pi. I might just be getting tired.

Because I'm only considering the top half of the loop in the integral.

 

[Dick]

Oh. So there's negative y's as well. I was getting tired. Carry on.

 

[elitespart]

lol no worries. Thank you again.