(7) Set up an iterated integral to compute the volume of the wedge of cheese cut...
(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
Do both questions and show all steps for good rating. Thanks. 7. Set up an iterated double integral to compute the volume of the solid bounded above by r2 y and below by the region R that is a triangle in the ry-plane with vertices (0,0), (0,3) and (5,3). z = (8) Do not evaluate. Exam 2-u ath 260-01 8. Set up a double integral in polar coordinates to find the volume of the solid bounded by zry 2 =...
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. Use cylindrical coordinates to SET UP the integral for the volume of the portion of the unit ball, 22 +232 + x2 < 1, above the plane z = 12 2. (a) Write in spherical coordinates the equations of the following surfaces: (i) x2 + y2 + x2 = 4 (ii) z = 3x2 + 3y2 (b) SET UP the integral in spherical coordinates for the volume of the solid inside the surface 22 + y2 + x2 =...
can someone explain the solution for this? 2. Set up an iterated integral for S. 6zdV L" SLO པ་ཁ་ནི where is the region inside the cylinder x2 + y2 - 9 and between the planes 2 = 4 + and 2 = 10. Evaluate the innermost part of the integral only. Solution: In cylindrical coordinates we can write this as 6z dx dr de Jo Jetron) evaluating the inner integral gives 6" / 33 ir con() dr de - 6...
(5 pts) Write an iterated integral for the volume of the tetrahedron cut from the first octant by the plane 1 + 4y + 8z = 8 in the order d.odydz.
7. (5 pts) By completing the limits and integrand, set up (without evaluating) an iterated inte-gral which represents the volume of the ice cream cone bounded by the cone z=√x2+y2andthe hemisphere z=√8−x2−y2using(a) Cartesian coordinates. 7. (5 pts) By completing the limits and integrand, set up (without evaluating) an iterated inte- gral which represents the volume of the ice cream cone bounded by the cone z = Vr2 + y2 and the hemisphere z = 18 - 22 - y2 using...
Use polar coordinates to find an iterated integral that represents the volume, V, of the solid described, and then find the volume of the solid.
SET UP a triple integral to find the volume of the solid in the first octant (all coordinates positive) that is below the pla 10. (8 pts.) SET UP a triple integral to find the volume of the solid in the first octant (all coordinates positive) that is below the plane x+3y + 2z =12.
Set up, but do not evaluate, a triple integral in cylindrical coordinates that gives the volume of the solid under the surface z = x2 + y2, above the xy- plane, and within the cylinder x2 + y2 = 2y.