Question 14 Evaluate the cylindrical coordinate integral. 7/2 12 1/r (cos 0) r dz dr de 6 1/12 O but + In 2 O 12nt + In 2 O 6 - In 2 O 12 - In 2Question 15 Evaluate the integral. 5 7 5r rde dz dr 3 O 490 O 980 3 O 245 O 1960 3Question 16 1 pts Solve the problem. Let D be the region bounded below by the cone 2 = le + 3-2 and above by the sphere z =l25 x?- 3-2 . Set up the triple integral in cylindrical coordinates that gives the volume of using the order of integration dz drde. 0 up a m 1[ 1!}! rdzdrde Question 17 1 pts Set up the iterated integral for evaluating [ [ [ f(x, 0, z) r dzar de over the given region D. D D is the right circular cylinder whose base is the circle r= 9 cos e in the xy-plane and whose top lies in the plane z = 10-x - y. O 7 9 sine 10- sin e- cos e f(r, 0, z) r dz dr de 27 9 cos @ 10- 1( cos 0 + sin e) f(r, 0, z) r dz dr de O 7 9 cos 0 10- 1( cos 0 + sin 0) f(r, 0, z) r dz dr de O 27 9 sine 10- sin e - cos 0 f(r, 0, z) r dz dr deQuestion 18 Evaluate the spherical coordinate integral. 71/2 71/3 9 sec o sin p cos p do do de 8 sec 12,325 8 O 7395 8 O 12,325 16 O 7395 16Question 19 1 pts Use a spherical coordinate integral to nd the volume of the given solid. the solid bounded below by the xy-plane, on the sides by the sphere 9: 10. and above by the cone T'L' F3 0 50011 C) 25011 0 20011 01(130 Question 20 1 pts Find the volume of the indicated region. the region bounded by the paraboloid z =x2 + _v2 and the cylinder 2:2 + _v2 =9 Question 21 1 pts Find the average value of F(x, y, z) over the given region. F(x, v, z) = 9x over the cube in the first octant bounded by the coordinate planes and the planes x =5, y=5, z =5 225 2 45 2 2025 2 O 405 2Question 22 Evaluate the integral by changing the order of integration in an appropriate way. Question 23 Find the Jacobian M or M (as appropriate) using the given equations. u, v) (in. V, w) x = 10u cost, _v= 1011 sinZv, z = 8w 0 1600u O 320u O lOOv O 320v Question 24 Sketch D and g(D) from the description of D and change of variables (x, y) = g(u, v). X = u cos v, y = u sin v where D is the rectangle 1 s us 2, O s v s - O None of these. O N n/2+ -1 -4 -3 -2 -1 2 3 4 -4 -3 -2 -1 1 2 3 4 X -2 O N g(D) -4 -3 -2 -1 1 2 3 4 -3 -2 -1 2 3 XQuestion 25 Use the given transformation to evaluate the integral. u=vx, V=V+X; \\'X r from R where R is the trapezoid with vertices at (2, 0], (3, 0], (0, 2], (0, 3] O 5(62- 1) 2e 0 5(62-1] 6e 0 5(62-1] 3e O Baez1) 4e Question 26 Use the given transformation to evaluate the integral. u = 2x + V - z, V=-x +y +Z, w=-x+y+2z; [ ] [ (2x+y-z)(z-x+ y)(2z-x+ y) dx dy dz, R where R is the parallelepiped bounded by the planes 2x + y - z =2, 2x+ y - Z=3, -x+ V + Z=4, -x+y+z=5, -x + y + 2z =3, -x + y + 2z =10 12,285 16 1365 2 1365 8 12,285 S