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# Integrals, moment of inertia, and Stokes theorem

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1
Evaluate
3&#8747;1
1-&#8747;-2
(x2y-2xy3)dydx

2
Correctly reverse the order of integration, then evaluate
1&#8747;0
1&#8747;y
xeydxdy

3
The plane region R is bounded by the graphs of y=x and y=x2 .
Find the volume over R and beneath the graph of f(x, y) = x + y.

4
Find the volume of the "ice cream cone" bounded by the sphere x2+y2+z2=1 and the cone
z
=
^/Â¯x2+y2-1

5
Find the moment of inertia around the z-axis of the solid bounded by
x = 0, y = 0, z = 0, y = 1 - x2, and 4x + 3y + 2z = 12, assume _(x,y,z)_1.
6
Evaluate &#8747;CP(x,y)dx+Q(x,y)dy
Given: P(x,y)=y2, Q(x,y)= 3x; C is the part of the graph of y=3x2 from (-1,3) to (2,12).

7
Use the divergence theorem to evaluate
&#8747;&#8747;s F?nds where n is the outer unit normal vector to the surface S. &#8747;&#8747;F = 3xi + 2y2j + 4zk;
S is the surface of the plane x + y + z = 6.
8
Use Stokes theorem to evaluate W = F?Tds where F(x, y, z) = 3yi - 2xj +4xk; C is the circle: x2 + y2 = 9, z = 4,
oriented counterclockwise as viewed from above.