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Repeat the above for | TT+ 7 F(x,y,z) = (x2 + y2) In this case express...
Consider the solid inside the hemispherez- 4-x2-y2, outside the cylinder x2+y2 -1 and y* , outside the cylinder x' +y 1 an above the plane z 1. Express the volume of this solid as a triple integral using the specified coordinate systerm Include a sketch of the solid. a. cylindrical coordinates. b. spherical coordinates.
Set up only
b. Find the volume of the solid bounded by z x2 y2 and z 3 in spherical coordinates. Set-up only (OJ 7a. Change to spherical coordinates. Set-up only.X 2. f(x, y,z)dzdxdy b. Find fffe'd/where E is the region bounded by z (x2 + y2)2 and z 1, inside x2 + y2 4 in cylindrical coordinates. Set-up only
b. Find the volume of the solid bounded by z x2 y2 and z 3 in spherical coordinates. Set-up only...
/ 3. (18 points) Consider the solid bounded above by x2 + y2 +ク= 15 and below by χ =-+ Set up the limits of integration for a triple integral of a function f(x, y, z) over this solid using (a) rectangular, (b) cylindrical, and (c) spherical coordinates.
/ 3. (18 points) Consider the solid bounded above by x2 + y2 +ク= 15 and below by χ =-+ Set up the limits of integration for a triple integral of a...
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...
(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).
Consider the solid inside the hemispherez- 4-x2-y2, outside the cylinder x2+y2 -1 and above the plane z 1.Express the volume of this solid as a triple integral using the specified coordinate system Include a sketch of the solid. ib. spherical coordinates
Consider the solid inside the hemispherez- 4-x2-y2, outside the cylinder x2+y2 -1 and above the plane z 1.Express the volume of this solid as a triple integral using the specified coordinate system Include a sketch of the solid. ib....
Q.7, as question above
7. Verify the divergence theorem for F(x, y,z) - by the sphere x2 + y2 + Z2-4. 4xöx +yy +4zőz and V is the region bounded (15 points)
7. Verify the divergence theorem for F(x, y,z) - by the sphere x2 + y2 + Z2-4. 4xöx +yy +4zőz and V is the region bounded (15 points)
5. Express the triple integral | f(x,y,z)dV as an iterated integral in cartesian coordinates. E is the region inside the sphere x2 + y2 + z2 = 2 and above the elliptic paraboloid z = x2 + y2
(5 pts each) Sketch the solid that is inside both z-x2+y 2. and x2 +y-4 with 1s z s 3. Then, given f(x.y,z) = x2 +y2+z2, use the specified coordinate system to set up the integral f(x.y,z)dV over the solid. using cylindrical coordinates а. b. using spherical coordinates