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Consider the solid inside the hemispherez- 4-x2-y2, outside the cylinder x2+y2 -1 and above the p...
Consider the solid inside the hemispherez- 4-x2-y2, outside the cylinder x2+y2 -1 and y* , outside...
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.
Question 8.6. The solid inside the sphere x? + y2 + 2? 3 4 and outside...
Question 8.6. The solid inside the sphere x? + y2 + 2? 3 4 and outside the cylinder I TY has density f(x, y, z) = typ • Write a triple integral (including the limits of integration) in cylindrical coordinates that gives the mass of this solid. • Write a triple integral (including the limits of integration) in spherical coordinates that gives the mass of this solid • Compute the mass of the solid using the integral that seems easier...
5. The solid E lies above the cone z = 3V x2 + y2, inside the...
5. The solid E lies above the cone z = 3V x2 + y2, inside the cylinder x2 + y2 = 4 and below the plane z = 8; see Fig.2. (a) Write the equations of those three surfaces in cylindrical coordinates and say in which horizontal plane the cone intersects the cylinder. (b) Set up a triple iterated integral in cylindrical coordinates, for this triple integral SSI r’dV
(5 pts each) Sketch the solid that is inside both z-x2+y 2. and x2 +y-4 with...
(5 pts each) Sketch the solid that is inside both z-x2+y 2. and x2 +y-4 with 1s z s 3. Then, given f(x.y,z) = x2 +y2+z2, use the specified coordinate system to set up the integral f(x.y,z)dV over the solid. using cylindrical coordinates а. b. using spherical coordinates
5. (2 points) Let S be the solid inside both x2+y2 = 16 and x2+y2 +...
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 +...
/ 3. (18 points) Consider the solid bounded above by x2 + y2 +ク= 15 and below by χ =-+ Set up th...
/ 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.
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.
1. (20 points) Suppose B is the solid region inside the sphere 2+ y2 +2 4, above the plane = 1, a...
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...
4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/...
4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/ and bounded below by the xy-plane.
4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/ and bounded below by the xy-plane.
[4] Let Q be the solid region in space below the plane z = 4, outside...
[4] Let Q be the solid region in space below the plane z = 4, outside the cylinder x2 + y2 = 1, and above the paraboloid z = x2 + y2 (see figure). 1 Express the integral =dV as an iterated integral in Ida x² + y² +2² cylindrical coordinates. Do not evaluate the integral.
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.
Question 8.6. The solid inside the sphere x? + y2 + 2? 3 4 and outside the cylinder I TY has density f(x, y, z) = typ • Write a triple integral (including the limits of integration) in cylindrical coordinates that gives the mass of this solid. • Write a triple integral (including the limits of integration) in spherical coordinates that gives the mass of this solid • Compute the mass of the solid using the integral that seems easier...
5. The solid E lies above the cone z = 3V x2 + y2, inside the cylinder x2 + y2 = 4 and below the plane z = 8; see Fig.2. (a) Write the equations of those three surfaces in cylindrical coordinates and say in which horizontal plane the cone intersects the cylinder. (b) Set up a triple iterated integral in cylindrical coordinates, for this triple integral SSI r’dV
(5 pts each) Sketch the solid that is inside both z-x2+y 2. and x2 +y-4 with 1s z s 3. Then, given f(x.y,z) = x2 +y2+z2, use the specified coordinate system to set up the integral f(x.y,z)dV over the solid. using cylindrical coordinates а. b. using spherical coordinates
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 +...
/ 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...
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...
4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/ and bounded below by the xy-plane.
4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/ and bounded below by the xy-plane.
[4] Let Q be the solid region in space below the plane z = 4, outside the cylinder x2 + y2 = 1, and above the paraboloid z = x2 + y2 (see figure). 1 Express the integral =dV as an iterated integral in Ida x² + y² +2² cylindrical coordinates. Do not evaluate the integral.
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