- #1
DottZakapa
- 239
- 17
- Homework Statement
- Let ##_\Omega \left\{ (x,y,z)\in R^3 : - \sqrt{3-y^2-z^2} \leq x \leq z+2 ,y^2+z^2 \leq 3 \right\} ##
and consider the function
##f(x,y,z)=y^2x+z^2x##
Represent the domain ##\Omega##
compute the vector field ##F=\nabla f##
compute the inward flux.
- Relevant Equations
- flux integration
Let ##_\Omega \left\{ (x,y,z)\in R^3 : - \sqrt{3-y^2-z^2} \leq x \leq z+2 ,y^2+z^2 \leq 3 \right\} ##
and consider the function
##f(x,y,z)=y^2x+z^2x##
Represent the domain ##\Omega##
compute the vector field ##F=\nabla f##
compute the inward flux.
So I've found that one is a cylinder of radius ##\sqrt 3##
the second figure is a sphere with radius ##\sqrt 3##
then there is a plane passing through z=2 and x=2
the sphere is inside the cylinder, and concerning the sphere i consider just the part above the x axes, can't see how the plane intersect the two
now,
i'm having problems on finding the intersections in order to find also the boundaries of integration, in truth I'm always struggling at this step.
How do I have to proceed?
and consider the function
##f(x,y,z)=y^2x+z^2x##
Represent the domain ##\Omega##
compute the vector field ##F=\nabla f##
compute the inward flux.
So I've found that one is a cylinder of radius ##\sqrt 3##
the second figure is a sphere with radius ##\sqrt 3##
then there is a plane passing through z=2 and x=2
the sphere is inside the cylinder, and concerning the sphere i consider just the part above the x axes, can't see how the plane intersect the two
now,
i'm having problems on finding the intersections in order to find also the boundaries of integration, in truth I'm always struggling at this step.
How do I have to proceed?