Hi. Could someone help me with this flux integral? I have to compute the flux of vector field F= (x+z)i hat + j hat + k hat through the surface S given by y=x^2+z^2 with 0 less than or equal to y which is less than or equal to (pi/2). If someone could walk me through the process, I would be extremely grateful. Thank you in advance.

Question

Hi. Could someone help me with this flux integral?  I have to compute the flux of vector field F= (x+z)i hat + j hat + k hat  through the surface S given by y=x^2+z^2 with 0 less than or equal to y which is less than or equal to (pi/2).  If someone could walk me through the process, I would be extremely grateful.  Thank you in advance.

anonymous · Answer

If someone could walk me through the detailed process, I would be extremely grateful.

anonymous · Answer

see the chat box :)

anonymous · Answer

what does latex use mean?

anonymous · Answer

wen we integrate the dot product of F with the unit normal vector of the surface,over the surface , in the interval 0<y<pi/2; 
to find the unit normal vector, find the gradient of the given surface.
imp.!: the equation y-x^2-z^2=0 or x^2+z^2-y=0 represents the same surface but gradient will giv vectors in opposite direction.

anonymous · Answer

now once u find n(cap) dot it with F and then integrate over ds. now for this ds we need to use the jacobian transformation vector |J|. the formula relating them is: 
 ds=|J|dxdydz...now once this's is found , u essentiall hav to substitue the limits and integrate. 
for knowing wat is jacobian,search net please. i can solve it,but i don't know how to type it in here :/