3.F=[y^2 x^2] 1<=x<=2 F(r(t))=[t^-2 t^2] dr=[1 -t^-2]dt b)Int(t^-1-1)dt(1..2) =-1/2 9.f(x,y)=sqrt(1+9xy) y=x^3 (0<=x<=1) Int(f(x,y)(0..1) 2.8 11.f(x,y,z)=z^2 128sqrt(29)/3 =230 13.sqrt(3)/2(e-1) =1.5 17.r(t)=[4t -3t 12t] 2<=t<=5 Int(r(t))(2..5) 39 dist between (8 -6 24) and (20 -15 60) 27.Int(ydx-xdy)(0..2) y=x^2 -8/3 29.Int((x-y)dx+(y-z)dy+zdz) line seg (0,0,0) to (1,4,4) 13/2 31.pi/2 35.2-(e-1)/e 1.(0,0,0) to (1,1,pi) f(x,y,z)=xysin(yz) 0 3.F(x,y)=[3 6y] f(x,y)=3x+3y^2 r(t)=[t 2t^-1] (1..4) -9/4 5.32e-1 9.F=y^2+(2xy+e^z)+ye^z f(x,y,z)=y^2x+e^zy 13.f(x,y,z)=ztanx+yz 15.F=[2xy+5 x^2-4z -4y] f(x,y,z)=x^2y+5x 17.16 19.f=x^2y-z r1=[t t 0](0..1) r2=[t t^2 0](0..1) =1