Set up the following integral in spherical coordinates, then integrate. CL * *zdedydz
A) solve this integral in cylindrical coordinates. b) set up the integral in spherical coordinates (without solving) 10 points Compute the following triple integral: 1/ 1.32 + plav JD where D is the region given by V x2 + y2 <2<2. Hint: z= V x2 + y2 is a cone.
Setup and eval the triple integral. spherical set up triple Integral and evaluate, in coordinates the solid inside the sphere x²+42+ z² = 44 and below the cone z= √²+ya. 8 de do do A c E
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 =...
6. Set up a triple integral using cylindrical or spherical coordinates to find the volume of the solid that lies between the surfaces 2 - 27- 2x - 2y' and 2=x-v Evaluate one of your triple integrals to find the exact volume of this solid.
arbitrary continuous function f(x, y, z) in spherical coordinates over the solid shown Set up the triple integral of an (Assume a 1 and b = 3.) f(x, у, z) dv = Ju/2 C фр Өр др arbitrary continuous function f(x, y, z) in spherical coordinates over the solid shown Set up the triple integral of an (Assume a 1 and b = 3.) f(x, у, z) dv = Ju/2 C фр Өр др
8, (5 points) Set up, but do not integrate, the line integral of the vector field G (z-y,3 the curve ya from(-1,-1) to (2,8). Simplify your integrand as much as possible. (5 points) Set up, but do not integrate, the line integral of the vector field GJ, 3 the curve y = x3 from (-1,-1) to (2,8). . Simplify your integrand as much as possible 8. (5 points) Set up, but do not integrate, the line integral of the vector...
ser up the triple integral in spherical coordinates to express the volume inside of a cone phi = pi/6 , and inside a sphere p=5
1. (13 pts.) Use spherical coordinates to set up the triple integral for the solid that is constructed from a portion of a sphere, x2 +y2 +Z2-1 that lies above the cone φ = π/4 . Do NOT evaluate. 1. (13 pts.) Use spherical coordinates to set up the triple integral for the solid that is constructed from a portion of a sphere, x2 +y2 +Z2-1 that lies above the cone φ = π/4 . Do NOT evaluate.
2 integral giving the surface area of the portion of (3) Set up, but do not evaluate, an 2m2+e above the triangle with vertices (0,0), (0,5) and (3,5). (4) Change the following points from rectangular coordinates into the specified coordi- nate systemn: (a) (-3,-3,9), Cylindrical Coordinates. (b) (V3,1,0), Spherical Coordinates. 2 integral giving the surface area of the portion of (3) Set up, but do not evaluate, an 2m2+e above the triangle with vertices (0,0), (0,5) and (3,5). (4) Change...
Set up only b. Find the volume of the solid bounded by z x2 y2 and z 3 in spherical coordinates. Set-up only (OJ 7a. Change to spherical coordinates. Set-up only.X 2. f(x, y,z)dzdxdy b. Find fffe'd/where E is the region bounded by z (x2 + y2)2 and z 1, inside x2 + y2 4 in cylindrical coordinates. Set-up only b. Find the volume of the solid bounded by z x2 y2 and z 3 in spherical coordinates. Set-up only...