(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 =
5. Use spherical coordinates to evaluate 1952/x + y? + dv ", over the solid bounded below by the cone z= V8 + y2 and, and above by the sphere z= 11- x2 - y2
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).
Evaluate the triple integral. 3z dV, where E is bounded by the cylinder y2 + z2 = 9 and the planes x = 0, y = 3x, and z = 0 in the first octant E
Use cylindrical coordinates to evaluate the triple integral ∭E √(x2+y2)dV where E is the solid bounded by the circular paraboloid z = 1-1(x2+y2) and the xy -plane.
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).
Evaluate ∫∫∫ E √ x 2 + y 2 + z 2 d V where E lies above the cone z = √ x 2 + y 2 and between the spheres x 2 + y 2 + z 2 = 1 and x 2 + y 2 + z 2 = 9 . df (76 KB) 2. Evaluate r2 + y2 + 22 dV x2 + y2 and between the spheres r? + y2 + 2 = 1 and...
Use spherical coordinates. Evaluate (4 − x2 − y2) dV, where H is the solid hemisphere x2 + y2 + z2 ≤ 16, z ≥ 0. H
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...
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...