P2-20 Given a vector function F=axy+a,x-y) P1(5,6) evaluate the integral Fdi from R(5,6)to P2(3,3)inFg235 a)along the direct path p P2(3,3 (2)}A b)along path PAP 5 Solution Fd=[ax+a(3x-y2)(a+a小)=对+(3x-y2) he equation of P, P2 is y=(x-1) PD阶Fd=+(3xy1]2(x1)+(2y+3-yb=10 P Pat②2 2=1(15-y xdx=18-24=-6x y A P1(5,6) P2 (3,3) 0 1 5 (1) (2) (2) 2 (3 ), F a xy a x y = + − x y F dl   1 P(5,6) 2 P (3,3) PP1 2 P AP 1 2 P.2-20 Given a vector function evaluate the integral from to in Fig.2-35 a)along the direct path b) along path 2 2 (3 ) ( ) (3 ) F dl a xy a x y a dx a dy xydx x y dy x y x y  = + −  + = + −     Solution The equation of P1P2 is 3 ( 1) 2 y x = − 2 2 1 1 2 3 2 2 5 6 3 (3 ) ( 1) (2 3 ) 10 2 P P P P Path F dl xydx x y dy x x dx y y dy  = + − = − + + − = −   ①       2 1 3 3 2 6 5 (15 ) 3 18 24 6. P P Path F dl y dy xdx  = − + = − = − ②   