Saturday

April 19, 2014

April 19, 2014

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...

**Related Questions**

Applied Maths - Given that position vector a=4i+2j, position vector b=13i+5j are...

Precalc - A line in space has the vector equation shown here. Fill in the blanks...

calculus - Triangle ABC is an equalateral triangle, with O it's centroid. a) ...

maths - Given that vector c and vector d are non zero vectors such that vector c...

Calculus - A line has Cartesian equation 3x-2y+3=0 .Determine a direction vector...

Calc. for Reiny - this can be done by projections of two vector. recall that the...

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,...

calculus - You are given the four points in the plane A = (-3,7), B = (-1,-6), C...

Calculus - You are given the four points in the plane A=(7,4) ,B=(9,-3) ,C=(13,5...