Find the flux of the field F=(-2x,3y,Z) across the surface S where S is the portion of y=(e^x) in the first octant that projects parallel to x-axis onto the rectangle with 1 <= y <= 2 and 0<= z <= 3. Define the unit normal vector n to point away from the yz-plane.
Im not exactly sure about...
so I was helping my friend today and ran into a problem.
the problem was to use Newtons method to approx. the intersection points of two graphs.
f=x^2
g=cosx
so I subtracted f-g, found the derivative and pluged in some guesses.
Except all of my guesses just blew upwards in values...
I need to find out how to solve this integral with the indicated changes/transformations.
int.[0 to 2/3]int[y to 2-2y]
(x+2y)e^(y-x)
dxdy
u=x+2y v=x-y
I know that the xy region is x=y y=0 and y=1- (x/2)
which is a triangle
so I created systems with U and V but can't get a new...
When I started out on this problem I attempted to use cylindrical coordinates.
The set up looked nice but integrated, no so nice
V=SSS rdzdrd(theta)
z from r^2 to rt. (2-r^2)
r from 0 to 1
and theta from 0 2pi
but when I got to integrating with respect to r it got weird, mabey a...
The part about spliting it into two intergrals doesn't really make sense to me. I have seen the solution to a similar one with a cone instead of a parabloid and it was done with one triple intergal not two added togreather. That's what you mean right?
I need to use spherical coordinates to try and find the volume of the region bounded by
x2 + y2 + z2 = 2 which converts to p=Sqrt.(2) a sphere
and
z = x2 + y2, a parabloid which I converted to cot(phi)csc(phi)=p
I hope the greek letters for these are comonly used...