12xz dV, where S is the solid region in the first octant (x, y, z >...
Please try helping with all three questions.......please 1 point) Integratef(x, y, z) 6xz over the region in the first octant (x,y, z 0) above the parabolic cylinder z = y2 and below the paraboloid Answer Find the volume of the solid in R3 bounded by y-x2 , x-уг, z-x + y + 24, and Z-0. Consider the triple integral fsPw xyz2 dV, where W is the region bounded by Write the triple integral as an iterated integral in the order...
JJJE Evaluate the triple integral (2 + xy) dV, where is the solid region above the paraboloid z = 22 + y2 and below the plane z = 9. O 817 O 547 O 1627 O 1087 O 727
(1 point) y2 and below the paraboloid 8xz over the region in the first octant(x, y, z 0) above the parabolic cylinder z Integrate f(x, y, z) Answer: (1 point) y2 and below the paraboloid 8xz over the region in the first octant(x, y, z 0) above the parabolic cylinder z Integrate f(x, y, z) Answer:
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...
[4] Let Q be the solid region in space below the plane z = 4, outside the cylinder x2 + y2 = 1, and above the paraboloid z = x2 + y2 (see figure). 1 Express the integral =dV as an iterated integral in Ida x² + y² +2² cylindrical coordinates. Do not evaluate the integral.
3. (34 pts) This question has three parts (a), (b) ad e atd are (a) Evaluste the integralJ)codA, where w (b) Evaluate I (y+2)dV, where E is the solid in the first octant that lies under the paraboloid 4y (c) Find The volume of the solid bounded by the paraboloids : 3a + 4-r-r 3y2 and z 3. (34 pts) This question has three parts (a), (b) ad e atd are (a) Evaluste the integralJ)codA, where w (b) Evaluate I...
Evaluate the triple integral ∭E(x+6y)dV∭E(x+6y)dV where EE is bounded by the parabolic cylinder y=6x2y=6x2 and the planes z=8x,y=12x,z=8x,y=12x, and z=0z=0.
All of 10 questions, please. 1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
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.