Homework Statement
Verify Greens theorem for the line integral ∫c xydx + x^2 dy where C is the triangle with vertices (0,0) (1,1) (2,0). This means show both sides of the theorem are the same.
Homework Equations
∫c <P,Q> dr = ∫∫dQ/dx -dP/dy dA
∫c xydx + x^2dy
The Attempt at a...
Okay, Why did you add the two equations? instead of subtract like in the first one. Aren't you supposed to do the same thing to both parts?
Hmmmm....I didn't know that about the final answer. Must have missed it in class. Now let's just clarify the middle part. Thanks and thanks in advance! :-).
First thing I did was eliminate x.
Rearranged the first equation to get, x+y-z=0 -------(3)
Multiplied (3) through by 2 to get, 2x+2y-2z=0 -------(4)
Subtracted (2) from (4) to get, 7y-z=-1 or y=(z-1)/7 ----(5)
Let z=t, so I got y=(t-1)/7.
Did the same thing for y, multiplying the first...
Homework Statement
Find the parametric equations for the line of intersection of two planes
Homework Equations
Equations for the two planes...
z=x+y,-------(1)
2x-5y-z=1 -----(2)
The Attempt at a Solution
My answers are not correct so I guess I'm going about it the wrong way. Someone...
Homework Statement
Find the mass and the center of mass of the solid E with the given density function ρ(x,y,z). E is bounded by the parabolic cylinder z = 1 – y2 and the planes x + 4z = 4, x=0, and z=0; ρ(x,y,z) =6.
m=?
x=?
y=?
z=?
Homework Equations
z = 1 – y2 and the planes x...
I don't understand. The question asks for the point of intersection of the two curves. Do I find the derivative, dot product? Just point me in the right direction please.