8. Use spherical coordinates to evaluate the following triple integral: az dx dy

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8. Use spherical coordinates to evaluate the following triple integral: az dx dy 9. Use the transformation u x-y, v x y to evaluate the double integral dA where R is the square with vertices (0, 2), (1, 1), 2, 2), and (1,3). 10. Find the surface area of the part of the surface f(x,y) x y that lies above the triangle with vertices (0, 0), (1,0), and (0, 2 f(x, y,z) dz dydx as an iterated triple integral with the 11. Rewrite the triple integral -1x2 0 order of integration as dxdydz. 12. Find the volume of the solid region that lies above the paraboloid z x2 y and below the half- cone x y 13. Use cylindrical coordinates to evaluate Tzdv, where E s the region enclosed by the paraboloid z x y' and the plane z 4 4. Evaluate the integral (x+ y)e dA by making an appropriate change of variables, where R is the rectangle enclosed by the lines x y 0, x- y 2, x+ y 0, and x y 3. 15. Find the average value of f(x, y) e Vx+e' over the rectangle 0,41 x [0,1]. 16. Let E be the pyramid with vertices A 0, 0,0. B(5,0,0, C(0,8, 0. and DC0, 0,400 Set up the integra x, y, z)dV as a triple iterated integral with the order of integration given by dxdy dz.

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