Friday

January 30, 2015

January 30, 2015

Posted by **Donny** on Monday, November 28, 2011 at 9:26pm.

- vector calculus -
**Steve**, Tuesday, November 29, 2011 at 12:20amIf F is a conservative field, then there will be a G such that F = ∇G.

If we let G(x,y) = 1/2 (x^2 + 2xy - y^2) then

∇G = 1/2 (2x dx + 2y dx + 2x dy - 2y dy)

= (x+y)dx + (x-y)dy

So, F is a conservative field and the line integral is path-independent.

So, just evaluate G at the limits of integration

G(1,2) = 1/2 (1+4-4) = 1/2

G(0,0) = 0

So, the integral evaluates to just 1/2

If I recall my vector calculus correctly...

**Answer this Question**

**Related Questions**

Multivariable Calculus - Green's Theorem - Compute the line integral of F = <...

Math - Hi, I need urgent help with these 3 integrals problems ... been stuck on ...

Calculus - for the function F(t)=ln(t^2), let f(t)=F'(t). Write the integral ...

Calculus - "Leave the answer as a definite integral, but indicate how it could ...

math - Use Green's Theorem to evaluate the line integral along the given ...

calculus - Evaluate the following line integral: ∮C[(4x^2+3x+5y)dx+(6x^2+...

calculus - Evaluate the following line integral: ∮C[(4x^2+3x+5y)dx+(6x^2+...

Math: Calculus - You are given the four points in the plane A = (5,-6), B = (9,1...

math/calculus - You are given the four points in the plane A(-3,6),B(0,-6),C(5,...

math/calculus - You are given the four points in the plane A(-3,6),B(0,-6),C(5,...