Unformatted text preview: MTH203
Review Problems_( EXAM3) / ' 1) Set up triple integral in cyliderical coordinates to find the volume of the solid that
lies inside the graphs of both x2 + y2 +22=16 and x2 +y2 — 4y = 0. 2) Let R be the solid region bounded byz = 10 —x2 —y2 artdz=x2 +y2—8. Set upa
triple integral for the volume of R.  3) Find theetvolume of the wedgeshaped region enclosed on the side by the cylinder
x = —cos(y). —7r/2 S y s ”/2, on the top by the plane 2 = —2x, below by the xyplane 4)Set up triple integral in cylindrical coordinate for the integral
I” ‘le + y2 + 2xy + z3 dV, Q is the first octant bounded by the cylinder x2 +y2 = 4 and
Q the planes 2 = 0 and z = 4. 5) Set up triple integral in spherical coordinates for the integral
[4]. 1H2 JET—ﬂ e‘("2+y’+zz>dzdydx.
0 —J 16—):2 —1/16—Jr2y2 6) For the vector field F(x, y) = xi +xyj, compute the line integral I Eat ;where C is V C
the part of the circle r=5 joining the point (5,0) to the point (0,—5) in the
counterclockwise direction. 7) Answer the following for the vector field F(x, y)
a) Show that F is conservative b) Find a potential function f(x,y) such that V f = F. 0) Evaluate I F.d ; where C is any smooth path from (0,2) to (2,1).
C 8) Evaluate f ydx —xdy + ydz, where C is the line segment connecting the point =< x—xy2,3 —x2y > C
(2,0, l) to the point (1,1,2).
9) Apply Greens Theorem to find f Re! ; where C
F(x,y) = 3xyi + 2xj and C is the boundary of the region bounded by the line
y = x and the parabola y = x2. . 10) Find work in two ways: Find the work done by F = (75% over the plane curve r(t) = (e’cos(t))i + (e‘sin(t))j from the point (1,0) to the point (e2”,0) in two ways:
a) By using the parametrization of the curve to evaluate the work integral
b) By evaluating a potential function for F. ...
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 Spring '08
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 Calculus

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