1. Evaluate the iterated integral

   ó õ p 0  ó õ x 0  sin( x) dydx

2. Find the volume of the solid bound between z = 0 and z = x+2y over

   R: x = 0 y = 0 x = 2 y = x2

3. Evaluate the following iterated integral by changing it from a Type I to a type II or vice versa:

   ó õ p 0  ó õ p x   sin( y) y dydx

4. Evaluate the following iterated integral by changing it from a Type I to a Type II or vice versa:

   ó õ 1 0  ó õ 1-x 0  sec2( 2y-y2) dydx

5. Find the mass of the cylinder between z = 0 and z = 1 over the interior of the unit circle if its mass density is given by r(x,y,z) = | y| .
6. What is the volume of the polyhedron with vertices (0,0,0) , ( 1,0,0) , ( 0,1,0) , (1,1,0) , ( 0,0,1) , and ( 0,1,1) ?
7. Suppose that the probability density for the time required to complete the ``A'' component of an exam is given by

   pA( x) = ì ï í ï î 0 if x < 0  1 30 e-x/30 if x ³ 0

   (time in minutes). Suppose the event of completing the ``B'' component of the exam has the same density. If the completion of the A and B sections are independent events, then what is the probability that a student will complete the entire exam (i.e., both sections) in less than an hour?
8. Evaluate by converting to polar coordinates:

   ó õ 1 0  ó õ Ö 2-x2 x  dydx

9. Evaluate by converting to polar coordinates

   ó õ 1 0  ó õ Ö 1-x2 1-x   dydx ( x2+y2)3/2

10. Use the coordinate transformation T( u,v) = á u,Öv ñ to evaluate

    ó õ Öp 0  ó õ Öp 0  ysin( y2) dy dx

11. Use the coordinate transformation T( u,v) = áu,ve^-u ñ to evaluate

    ó õ 1 0  ó õ 1 0  yex dy dx

12. Suppose r( x,y,z) = xz( 1-y) coulombs per cubic meter is the charge density of a ''charge cloud'' contained in the ''box'' given by [ 0,1] ×[ 0,1] ×[0,1] . What is the total charge inside the box?
13. Evaluate by converting to spherical coordinates

    ó õ 1 -1  ó õ Ö 1-x2 -Ö 1-x2 ó õ Ö 2-x2-y2 Ö x2+y2  dzdydz z x2+y2+z2

14. What is the mass of the cone x²+y² = z² between z = 0 and z = 1 if the mass density is constant at m = 4 kg per cubic meter?