1. Solid Volume

Hey fellow users!

One more time, I just didn't seen to find the answer :S

Volume of the solid got by rotation, around axis x, of the group of all (x,y) such as

Question 1. 0 <= y <= x and x² + y² <= 2
Question 2. y >= x² and x² + y² <= 2

Thanks!

2. Re: Solid Volume

What have you tried? Did you identify the deisred region in the First Quadrant?

Important points are the Origin, the intersection of the line and the circle, and the intersection of the circle and the x-axis. Please identify these points.

3. Re: Solid Volume

I'm starting at this, so i don't understand the process. Well, first i need to find the area in the intersection of the functions.
How can i get the funcions of the first question? And the limits of the volume integral?

4. Re: Solid Volume

Don't take this as a personal insult. It's just a little reality therapy. If you cannot find the intersection of y = x and x^2 + y^2 = 2 in the First Quadrant, you should not be in this class.

Perhaps it would be more clear to write it this way:

0 <= y
0 <= x
y <= x
x^2 + y^2 = 2

Now, can you find the three important points? (0,0) and two more.