finding volume

[tallman2366]

Use a double integral to find the volume of the solid bounded by the paraboloid z=4-x^2-2y^2 and the xy plane.

 

[tallman2366]

Use a double integral to find the volume of the solid bounded by the paraboloid z=4-x^2-2y^2 and the xy plane.

I know how to integrate , but I do not know if I can change the integrand into polar. I know that r^2= x^2 +y^2 but this says 2y^2 , that is where I am stuck.

 

[raquelc]

On the plane xy, z=0 , 4=x^2+2y^2...or 1=x^2/4+y^2/2. Does that look familiar?
From there you can determine the boundaries of your integral

 

[HallsofIvy]

In polar coordinates, the circle centered at the origin with radius 2 can be covered by taking r from 0 to 2 and \(\displaystyle \theta\) from 0 to \(\displaystyle 2\pi\).

 

[tallman2366]

In polar coordinates, the circle centered at the origin with radius 2 can be covered by taking r from 0 to 2 and \(\displaystyle \theta\) from 0 to \(\displaystyle 2\pi\).

Thank you very much

In polar coordinates, the circle centered at the origin with radius 2 can be covered by taking r from 0 to 2 and \(\displaystyle \theta\) from 0 to \(\displaystyle 2\pi\).

Thank you very much

 

[tallman2366]

Thank you very much

Thank you very much

now I would have to convert

Thank you very much

Thank you very much

now i would have to convert z=4-X^2 -2y^2 to polar

 

[tallman2366]

not quite sure how to do that

so if you have 4= x^2 + 2y^2 how would you convert that to polar

 

[Steven G]

x=rcos theta and y = rain theta??

 

[Deleted member 4993]

x=rcos theta and y = rain theta??

What is that??

 

[topsquark]

What is that??

It's the sequel to "Rain Man" only this time he's not counting cards, he's doing trig.

-Dan

 

[Steven G]

x=rcos theta and y = rain theta??

r=rsin theta

 

[tallman2366]

I have z= 4-x^2- 2y^2 which is a paraboloid
I need to change this to polar
I know that x= rcos theta
y+= rsin theta
I need to find thevolume bounded by the paraboloid and the xy plane
z= 0 on the xy plane
4-x^2-2y^2 = 0
4= x^2 + 2y^2
divide each side by 4 and you get
1= x^2/4 + 1/2 y^2
1 - (r cos theta )^2 + 2 (r sintheta)^2/4
DO not know it I am doing it right, any help would be appreciated
Thanks

 

[Steven G]

That last express is not correct. What happened to the equations which you had all along?

 

[tallman2366]

Not sure what you mean

 

[Steven G]

Not right, wrong, has a mistake....

All the other lines are equations, that is they have an equal sign. The last line is an expression, not an equation, as it has no equal sign. What happened there?