Question

need a little help here. thanks.

Answer 1

@ganeshie8

Answer 2

\[\large\int\limits_{x_1,y_1}^{x_2,y_2}\nabla f(x,y)\,\mathrm dy\,\mathrm dx=f(x_2,y_2)-f(x_1,y_1)\]

Answer 3

So, find the value on the table that corresponds to (4,1), and from this, take away the value that corresponds to (0,3)

Answer 4

for part b), the start and endpoints of a circular path are the same

Answer 5

starting point is 4,2 and end point is 4,2

Answer 6

which is just 0

Answer 7

yeah, with the start and endpoints equal the integral of the gradient will be zero

Answer 8

cool. thanks!

Answer 9

what did you get for part a)?

Answer 10

that means the field is path independent, the work done doesn't depend on the path you take.. and consequently work done along any closed loop will be 0 too

Answer 11

-4

Answer 12

\[\ddot\smile\]