Calculus 3: Evaluate the line integral, where C is the given curve.

Evaluate the line integral, where C is the given curve.

C xy dx (x - y)dy

C consists of line segments from (0, 0) to (5, 0) and from (5, 0) to (6, 2).



Can someone walk me through this. I got 298.5 for my answer but that is incorrect.

Thank you in advance.
c xy dx (x - y) dy



from (0,0) to (5,0)

x = 5t ; y = 0 ; 0 t 1 ........... in parametric form

dx = 5 dt ; dy = 0

c xy dx (x - y) dy

= 5t (0) 5 dt (5t - 0) (0) dt

= 0



from (5,0) to (6,2)

x = 5 t ; y = 2t ; 0 t 1 ..... in parametric form

dx = dt; dy = 2 dt

c xy dx (x - y) dy

= (5 t)(2t) dt ((5 t) - 2t) 2 dt

= 2 t 4t 5 dt

= 2/3 t 4 t 10 t ..... from 0 to 1

= 2/3 4 10

= 44/3



Answer: 44/3