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Math · Calculus
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Q-1) Evaluate the line integral Jaxyvd*+ yzdy + 3dz where Cis the curve with parametric equation x-+1, y 2t and z- 1-t, 0stS1. Q-2) a) Show that the line integral is independent of path (2x++(5+2yax)dy b) Evaluate the line integra2x+yx (5+2yx) dy where Cis any curve from the point A(1,1) and B(2,4) to Q-3) (10 points) Use Greens Theorem to evaluate the line integral ф(2)xpr+(y + C is positively oriented boundary of the region bounded by y 2vx, x 4 and x- axis.
Q-4) (20 points) Evaluate the surface integral J(* +y) ds where Sis the portion of the Plane x+z-1 as shown in the figure by the shaded surface.
Q-5) Given F(x, y,z)-3yxi +4zyj+ak. Then evaluate a) (10 points) curl F = V× F b) (10 points) dívF=V.F Q-6) (20 points) Use Divergence Theorem to evaluate the outward flux JF ndS of the vector field Fx,y,2)-xy iz j+zx k where S is the surface of the first octant portion of the region Q bounded by z-9-y and planesx 0 and x-2. (see the figure given below). 9 9-2 ac
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