5. Express the triple integral | f(x,y,z)dV as an iterated integral in cartesian coordinates. E is...
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...
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)
4. (5 points) Express the integral JI f(x, y, z) dV as an iterated integral in 6 different ways, where E is the solid region bounded by y2 + z-9. x--2, and x-2. 4. (5 points) Express the integral JI f(x, y, z) dV as an iterated integral in 6 different ways, where E is the solid region bounded by y2 + z-9. x--2, and x-2.
Please explain steps 3. Consider the triple integral , g(x, y, z)dV, where E is the solid bounded above by the sphere x2 + y2 + z2 = 18 and below by the cone z= x2 + y2. a) Set up the triple integral in rectangular coordinates (x,y,z). b) Set up the triple integral in cylindrical coordinates (r,0,z). c) Set up the triple integral in spherical coordinates (0,0,0).
10. Consider the integral (x + y + z) dV where D is the volume inside the sphere x2 + y2 + x2 = 9 and above the plane z = 1. (a) (3 marks) Express I as an iterated integral using Cartesian coordinates with the order of integration z, x and y. DO NOT EVALUATE THIS INTEGRAL. (b) (3 marks) Express I as an iterated integral using spherical coordinates with the order of integration p, 0, and 0. DO...
Use spherical coordinates to calculate the triple integral of f(x, y, z) = y over the region x2 + y2 + z2 < 3, x, y, z < 0. (Use symbolic notation and fractions where needed.) S S lw y DV = help (fractions)
(1 point) Use spherical coordinates to evaluate the triple integral dV, e-(x+y+z) E Vx2 + y2 + z2 where E is the region bounded by the spheres x² + y2 + z2 = 4 and x² + y2 + z2 16. Answer =
(16) (7 points) Set up an iterated integral of f (x, y, z) = x2 + y2 + z2 over the solid region shown below. Use the spherical coordinates. N 1 y - One-eighth sphere
Consider the triple integral SISE g(x,y,z)d), where E is the solid bounded above by the sphere x2 + y2 + z2 = 18 and below by the cone z? = x2 + y2. a) Set up the triple integral in rectangular coordinates (x,y,z). b) Set up the triple integral in cylindrical coordinates (r, 0,z). c) Set up the triple integral in spherical coordinates (2,0,0).
Use cylindrical coordinates to evaluate the triple integral J Vi +y2 dV, where E is the solid bounded by the circular paraboloid z 16 -1(z2 +y2) and the xy-plane.