Question 24 1 Calculate the iterated integral. So S," (x + 2y)dady 3 20 None of...
The value of the iterated integral z S' ()dyda - Select one: A. None of these answers B. 0 C. In( )3 D. In(3) E. In(Ķ) 3
12 Problem 1. Calculate the iterated integral S(x+e) dx dy. 01
Write an iterated integral for SSS fex,y,z) av. S = {(x, y, z): 0 sxs8,0 sy s5,0<zs (5 - 6x - 2y)} 5 S 5-6x - 2y f(x, y, z) dz dy dx 5 8 5 f(x, y, z) dz dy dx s 8 5 5 - 6x - 2y f(x, y, z) dz dy dx 5 666 8 5 5 - 6x - 2y f(x, y, z) dx dy dz
6. (10 points) Express the triple integral / S / F(x,y,z)dV as an iterated integral in cartesian coor- dinates. E is the region inside the cylinder x2 + y2 = 1, above the xyplane and below the plane x+y+z=2. (DO NOT EVALUATE THE INTEGRAL)
For the described solid S, write the triple integral f(x,y, z)dV as an iterated integral in (i) rectangular coordinates (x,y, z); (ii) cylindrical coordinates (r, 0, 2); (iii) spherical coordinates (p, φ,0). a. Inside the sphere 2 +3+224 and above the conezV b. Inside the sphere x2 + y2 + 22-12 and above the paraboloid z 2 2 + y2. c. Inside the sphere 2,2 + y2 + z2-2 and above the surface z-(z2 + y2)1/4 d. Inside the sphere...
5. (10 points) Express the triple integral | | . f(x,y,z)dv as an iterated integral in cartesian coor- dinates. E is the region inside the cylinder x2 + y2 = 1, above the xyplane and below the plane x+y+z=. (DO NOT EVALUATE THE INTEGRAL)
Question 7 5 pts each Write iterated integrals for each of the given calu lations. Do not evaluate. (A) The integral of f(x, )212y over the domain D: 2 y 20. (B) The integral of f(x, y, z) = 12x + 3 over the volume contained in the first octant and below the graph z 8-y 2 (C) The mass of an object occupying the region bounded between the sur faces x2 + y2 + Z2 = 16 and z...
6. (10 points) Express the triple integral SS 5, 8(x,y,z}dV as an iterated integral in cartesian coor- dinates. E is the region inside the cylinder x2 + y2 = 1, above the xyplane and below the plane x+y+z=2. (DO NOT EVALUATE THE INTEGRAL)
Please Answer the Following Questions (SHOW ALL WORK) 1. 2. 3. 4. Write an iterated integral for SSSo flexy.z)dV where D is a sphere of radius 3 centered at (0,0,0). Use the order dx dz dy. Choose the correct answer below. 3 3 3 OA. S S f(x,y,z) dx dz dy -3 -3 -3 3 OB. S 19-x2 19-32-22 s f(x,y,z) dy dz dx 19-x2 - 19-2-22 s -3 3 3 3 oc. S S [ f(x,y,z) dy dz dx...
6. (10 points) Express the triple integral || ! f(x,y,z)AV as an iterated integral in cartesian coor- dinates. E is the region inside the cylinder x2 + y2 1, above the xyplane and below the plane x+y+z = 2. (DO NOT EVALUATE THE INTEGRAL)
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