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These are questions asked by heomoi

graph the vector field F and the curve C to guess whether the line integral of F over C is positive or negative or zero. then evaluate the line integral F(x,y) = (x/sqrt(x^2+y^2)i + (y/sqrt(x^2+y^2)j C is the parabola y =1 +x^2 from (-1,2) to (1,2)
plot the gradient vector field and the contour map of f f(x,y) = sinx + siny
can anyone help me to plot that vector field of F(x,y) = (y^2 -2xy)i + (3xy -6x^2)j
the cylinder r = a*cos(O) cut out of the sphere of radius a centered at origin. any help. thanks
Graph the solid bounded by the plane x+y+z =1 and paraboloid z=4-x^2 -y^2, and find the volume. here what i tried, but i cannot get the volume > f := x+y-1; > g := 4-x^2-y^2; > plot3d({f, g}, x = -2 .. 2, y = -sqrt(1-x^2) .. sqrt(1-x^2), axes = boxed); V:=Doubleint(g-f,y=-sqrt(1-x^2)..sqrt(1-x^2),x=-2..2): V=value(V);
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