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6. Set up a triple integral using cylindrical or spherical coordinates to find the volume of...
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.
4. Using spherical coordinates, evaluate the triple integral: ry: dl, where E lies between the spheres r2+94:2-4 and r2+92+ะ2-16 and above the cone V+v) or Recommend separating! 5. Using spherical coordinates, find the volume of the solid that lies within the sphere r2+y2+2 9, above the ry-plane, and below the cone ะ-V/r2 + y2 Reconnnend separating! 6. Using spherical coordinates, evaluate the triple integral: 2 + dV where E is the portion of the solid ball 2+2+2 s 4 that...
Question Use cylindrical coordinates to set up the triple integral needed to find the volume of the solid bounded above by the xy-plane, below by the cone z = x2 + y2 , and on the sides by the cylinder x2 + y2 = 4. a) 06.* %* ["dz dr do b) $* * S*rde de do JO 0% ] raz dr do a) $** [Lºdz dr do 0906.*|*Lºrdz dr do 2 po dz dr do Jo J- O J-...
6. (12pts) Consider the solid that is above the xy-plane, bounded above by =/4-x-y and below by +y a. Sketch the solid formed by the given surfaces b. Set up in rectangular coordinates the triple integral that represents the yolume of the solid. Sketch the appropriate projection. Do NOT evaluate the integrals. (Hint: Let dV- d dy de) c. Set up in cylindrical coordinates the triple integral that represents the volume of the solid. Sketch the appropriate projection. Do NOT...
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
Use rectangular, cylindrical and spherical coordinates to set up the triple integrals representing the volume of the region bounded below by the xy plane, bounded above by the sphere with radius and centered at the origin the equation of the sphere is x2 + y2 + z2-R2), and outside the cylinder with the equation (x - 1)2 +y2-1 (5 pts each) Find the volume by solving one of the triple integrals from above.( 5 pts) Total of 20 pts) Use...
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 =...
Find the volume of the given solid region in the first octant bounded by the plane 2x + 2y + 4z4 and the coordinate planes, using triple integrals 0.0(020 Complete the triple integral below used to find the volume of the given solid region. Note the order of integration dz dy dx. dz dy dx Use a triple integral to find the volume of the solid bounded by the surfaces z-2e and z 2 over the rectangle (x.y): 0 sxs1,...
1. Convert the point ( 215 7.) from cylindrical to spherical coordinates. 2. Set up a triple integral, but do NOT evaluate, to find the volume of the solid in the first octant bounded by the coordinate planes and the plane 3x + 6y + 4z = 12. 1 3. Locate all relative maxima, relative minima, and saddle points of f(x,y) = x2 + 2y2 – x?y.
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.