8. Evaluate the triple integral of the function f(x, y, z) = 6x over the solid...
Evaluate the triple integral. ∭E5xy dV, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded by the curves y = √x, y = 0, and x = 1
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...
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...
======== triple integral problem. provide full answers in detail to get upvote. thanks. Evaluate the triple integral y dV, where E is the solid that lies under the plane x+z = 1° and above the triangle with vertices at (0, 0), (2, 1), (0, 3) Evaluate the triple integral y dV, where E is the solid that lies under the plane x+z = 1° and above the triangle with vertices at (0, 0), (2, 1), (0, 3)
+-/1 points SCalcET8 15.6.013. My Notes Evaluate the triple integral. here E lies under the plane z 1+x+ y and above the region in the xy-plane bounded by the curves y Vx, y 0, and x 1 3xy dV, Need Help? Read It Talk to a Tutor Watch It Submit Answer Practice Another Version
Set up the triple integral of an arbitrary continuous function f(x, y, z) in cylindrical or spherical coordinates over each solid shown & described below. i.e., Fill in the six limits of integration and the blank at the end. There is nothing to evaluate. (a) The solid is between the top hemisphere of the ball of radius 2 centered at the origin and the inside of the upper half cone z = Vx2 + y2. r?+ y2 + = 4...
6. Set up, but do not evaluate, an iterated integral that gives the volume of the solid region that lies below the paraboloid z =エ2 + V2 and above the region in the zy-plane bounded by the curves-8a2 and i-z. 6. Set up, but do not evaluate, an iterated integral that gives the volume of the solid region that lies below the paraboloid z =エ2 + V2 and above the region in the zy-plane bounded by the curves-8a2 and i-z.
(1 point) Evaluate the triple integral of f(x, y, z) = cos(x2 + y²) over the solid cylinder with height 2 and with base of radius 1 centered on the z axis at z = -2. Integral = 6pisin(4)
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)
please answer question 3. 1. Find the integral of the function f(x, y, z)xy+2 z over the region enclosed by the planex +y+z 2 2. Find the volume and center of gravity for the solid in the first octant (x 20, y 20, z20) bounded by 3. Find the center of mass for the solid hemisphere centered at the origin with radius a if the density and the coordinate planes z0,y 0, and x0 the parabolic ellipsoid Z-4-r-y. function is...