02. (10+10+5=25 points) The region E is the solid hemisphere x2 + y2 + 59.220 a)...
5. (2 points) Let S be the solid inside both x2+y2 = 16 and x2+y2 + z2 = 32. Consider (a) Write an iterated integral for the triple integral in rectangular coordinates. (b) Write an iterated integral for the triple integral in cylindrical coordinates. (c) Write an iterated integral for the triple integral in spherical coordinates. (d) Evaluate one of the above iterated integrals. 5. (2 points) Let S be the solid inside both x2+y2 = 16 and x2+y2 +...
Consider the solid inside the hemispherez- 4-x2-y2, outside the cylinder x2+y2 -1 and above the plane z 1.Express the volume of this solid as a triple integral using the specified coordinate system Include a sketch of the solid. ib. spherical coordinates Consider the solid inside the hemispherez- 4-x2-y2, outside the cylinder x2+y2 -1 and above the plane z 1.Express the volume of this solid as a triple integral using the specified coordinate system Include a sketch of the solid. ib....
Consider the solid inside the hemispherez- 4-x2-y2, outside the cylinder x2+y2 -1 and y* , outside the cylinder x' +y 1 an above the plane z 1. Express the volume of this solid as a triple integral using the specified coordinate systerm Include a sketch of the solid. a. cylindrical coordinates. b. spherical coordinates.
/ 3. (18 points) Consider the solid bounded above by x2 + y2 +ク= 15 and below by χ =-+ Set up the limits of integration for a triple integral of a function f(x, y, z) over this solid using (a) rectangular, (b) cylindrical, and (c) spherical coordinates. / 3. (18 points) Consider the solid bounded above by x2 + y2 +ク= 15 and below by χ =-+ Set up the limits of integration for a triple integral of a...
Consider the solid enclosed by x2 + y2 + z2 = 2z and z2 = 3(x2 + y2) in the 1st octant. a) Set up a triple integral using spherical coordinates that can be used to find the volume of the solid. Clearly indicate how you get the limits on each integral used. b) Using technology, or otherwise, evaluate the triple integral to find the volume of the solid.
Let D be the solid spherical "cap" given by x2 + y2 + z2 < 16 and 2 > 1. Set up, but do not evaluate, a triple integral representing the volume of D in cylindrical coordinates.
Please show all steps. Thank you, need to verify what I'm doing wrong. 1. (20 points) Suppose B is the solid region inside the sphere 2+ y2 +2 4, above the plane = 1, and in the first octant (z, y, z 0)、z, y and z are measured in meters and the density over B is given by the function p(z, y, z)-(12 + y2 + ?)-1 kg/m3 (a) Set up and write the triple integral that gives the mass...
A solid is bounded above by a portion of the hemisphere z= 2 – – 72 . And below by the cone z = 2 + y2 , with a < 0 and y < 0. Part a: Express the volume of the solid as a triple integral involving 2, y and z. Part b: Express the volume of the solid as a triple integral in cylindrical coordinates. Parte: Express the volume of the solid as a triple integral in...
Use spherical coordinates. Evaluate (4 − x2 − y2) dV, where H is the solid hemisphere x2 + y2 + z2 ≤ 16, z ≥ 0. H
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.