Evaluate the line integral ∫5ydx+2xdy where C is the straight line path from (2,4) to (5,9).

Answer 1

the line from (2,4) to (5,9) can be written as
x = 3t+2
y = 5t+4
So, using the path indicated, with 0 <= t <= 1
∫5ydx+2xdy
= ∫(5y dx/dt + 2x dy/dt) dt
= ∫5(5t+4)(3) + 2(3t+2)(5) dt
= ∫(105t+80) dt
= 52.5 t^2 + 80t [0,1]
= 132.5