1. ## volume

express as a repeated integral the volume of the cone bounded above by z=2 and below by z= (x^2 +Y^2) ^(1/2) by taking slices at fixed x.

i was trying to find the limits for x and y and z but i got stuck..

since im taking slices at fixed x, -2<x<2

and (x^2 +Y^2) ^(1/2) <z<2

but i do not know how to find the limits for y.

thanks

2. Originally Posted by alexandrabel90
express as a repeated integral the volume of the cone bounded above by z=2 and below by z= (x^2 +Y^2) ^(1/2) by taking slices at fixed x.

i was trying to find the limits for x and y and z but i got stuck..

since im taking slices at fixed x, -2<x<2

and (x^2 +Y^2) ^(1/2) <z<2

but i do not know how to find the limits for y.

thanks
Ok, the limits +/-2 for the outermost integral with respect to x are right, now just imagine that an x from that range has been chosen. The y over which the next inner integral varies must still satisfy $\sqrt{x^2+y^2}\leq z\leq 2$.

Since z can still be chosen to be from a suitably small intervall, the relevant condition for the limits for y is $\sqrt{x^2+y^2}\leq 2$, from which it follows that $y^2\leq 4-x^2$, in other words $-\sqrt{4-x^2}\leq y\leq +\sqrt{4-x^2}$, agreed?

3. thanks for the explanation...

because my notes wrote that the range of y should be

-(2-x^2) ^(1/2) < y< (2-x^2) ^(1/2) ...and i couldnt figure out why...

i think there should be something wrong with it..

4. Originally Posted by Failure
Ok, the limits +/-2 for the outermost integral with respect to x are right, now just imagine that an x from that range has been chosen. The y over which the next inner integral varies must still satisfy $\sqrt{x^2+y^2}\leq z\leq 2$.

Since z can still be chosen to be from a suitably small intervall, the relevant condition for the limits for y is $\sqrt{x^2+y^2}\leq 2$, from which it follows that $y^2\leq 4-x^2$, in other words $-\sqrt{4-x^2}\leq y\leq +\sqrt{4-x^2}$, agreed?
I agree with this

Originally Posted by alexandrabel90
thanks for the explanation...

because my notes wrote that the range of y should be

-(2-x^2) ^(1/2) < y< (2-x^2) ^(1/2) ...and i couldnt figure out why...

i think there should be something wrong with it..
I think your prof must have a mistake. Seeing as this is a cylindrical cone would we not want to do this in cylindrical co-ordinates anyways?

5. thank you! (: