Question

Calculate the line integral of the vector field  F  = xy i  + (x − y) j  along C, the triangle composed of three segments. C1 is the line segment from (4, 0) to (-4, 0). C2 is the line segment from (-4, 0) to (0, 4). C3 is the line segment from (0, 4) to (4, 0).

Answer 1

Explanation:

Value of the line integral for C1: 0

Value of the line integral for C2: -27/2

Value of the line integral for C3: 9/2

Value of the line integral for C4: -18/2

Answer 2

Thank you for posting your question here at brianly. I hope the answer will help you. Below is the solution:

or segment from (4,0) to (-4,0), y is always zero because straight segment.
in that case x*y=x*0=0
and x+y=x+0=x
if you choose x=4-t where t goes from 0 to 8 you should get
r(t)=0i+(4-t)j