(1 point) Evaluate the triple integral I2(x2 +y2)dV where D is the region inside the parabolid z 4-x2-y2 and inside the first octant2 0, 0,z0 B. I 12 D. I E. I (1 point) Evaluate the triple inte...
Evaluate the triple integral I=∭D(x2+y2)dV where D is the region inside the cone z=x2+y2−−−−−−√, below the plane z=2 and inside the first octant x≥0,y≥0,z≥0. A. I=0 B. I=(π/20)2^5 C. I=(π/10)2^5 D. I=π2^5 E. I=(π/40)^25
Evaluate the integral, where E is the region that lies inside the cylinder x2 + y2 = 4 and between the planes z = -1 and z = 0. Use cylindrical coordinates. SSSE V.x2 + y2 DV =
(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 =
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.
(1 point) Evaluate the triple integral redV where E is the region bounded by the parabolic cylinder z 1-y2 and the planesz = 0, x = i, and x =-1. (1 point) Evaluate the triple integral redV where E is the region bounded by the parabolic cylinder z 1-y2 and the planesz = 0, x = i, and x =-1.
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. Evaluate SIS x2 + y2 dv, where E is the region that lies inside the cylinder x2 + y2 = 4 and between the planes z = 3 and z = 12. x
/// (1 point) Evaluate the triple integral 1 yd where D is the region in the first octant (z > 0, y 0,2 2 0 below the plane z = 1 y and with z /// (1 point) Evaluate the triple integral 1 yd where D is the region in the first octant (z > 0, y 0,2 2 0 below the plane z = 1 y and with z
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...
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...