anyone?
Hi, I'm having a little trouble to solve these problems. May anyone help me please?
What is the area of the spherical surface X^2+Y^2+Z^2=9 inside the cylinder
X^2+Y^2=3x ?
What is the area of the spherical surface X^2+Y^2+Z^2=9 inside the cylindrical X^2+Y^2=4 ?
What is the area of the spherical surface X^2+Y^2+Z^2=16 inside the cylindrical Y^2+Z^2=4Z ?
Thanks, and sorry for my English because it is not my native language
When you draw it, the approach becomes immediately clear right? Just integrate under that section of intersection:
where:
Just complete the square in to get D.
I haven't actually tried to do the integration though. May need to use spherical or other means to evaluate it. Also, it's easy to draw. Here's the Mathematica code:
Code:pic1 = ContourPlot3D[{x^2 + y^2 + z^2 == 9, x^2 + y^2 == 3*x}, {x, -3, 3}, {y, -3, 3}, {z, -3, 3}, ContourStyle -> {Opacity[0.4], LightPurple}]
So what's the integral you get? We can just integrate over the first quadrant right since it's symmetric and just multiply by 2 and that's just the top so multiply by 2 again but for now, just the top over the first quadrant I get:
where we'll set be the surface area over the top part just over the first quadrant.
The x^2+y^2 part looks amendable to polar coordinates. Mathematica reports for that integral . Don't see immediately how to do the integration though.
Yeah, I got the same integration. The problem is that after I tried to put in polar coordinates, the integration that came is very difficult to solve without cas
X=1,5 + R.Cos(A)
Y=R.Sen(A)
0<=R<=1.5
0<=A<=pi
it would be:
2*intg*intg R/(Sqrt(-Rcos(A)-R^2+6.75))drda
I stop here; don't know how to solve, or if this is right
Hey, this ain't no hill:
You can do the first part right:
That's just an inverse sine but I ran into problems with that so I converted it to an inverse tan. When I simplify it and apply the limits, I get for the outer integral::
Now, I think we can integrate that by parts. You'll need to check all this cus' I went through it quick but I think the principle is sound.