Evaluate ∫∫∫T 2xy dx dy dz where T is the solid in the first octant bounded...
Evaluate ∫∫∫T 2xy dx dy dz where T is the solid in the first octant bounded above by the cylinder z = 4 − x^2 below by the x, y-plane, and on the sides by the planes x =0, y = 2x and y = 4. Answer: ∫ (4, 0) ∫ (y/2, 0) ∫ (4−x^2, 0) 2xy dz dx dy = ∫ (2, 0) ∫ (4, 2x) ∫ (4−x^2, 0) 2xy dz dy dx = 128/3
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Evaluate ∫∫∫T 2xy dx dy dz where T is the solid in the first
octant bounded...
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 f...
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,...
Question 11 A solid in the first octant, bounded by the coordinate planes, the plane (x=...
Question 11 A solid in the first octant, bounded by the coordinate planes, the plane (x= a) and the curve (z=1-y). Find the volume of the solid by using : #-Double integration technique (Use order dy dx) a=51 b-Triple integration technique (Use order dz dy dx) ..
10) Calculate the integral zdac dy dz where D is bounded by the planes x =...
10) Calculate the integral zdac dy dz where D is bounded by the planes x = - 0, y = 0, z = 0, z = 1, and the cylinder x2 + y2 = 1 with x > 0 and y> 0. 11) Let y be the boundary of the rectangle with sides x = 1, y = 2, x = 3 and y = 3. Use Green's theorem to evaluate the following integral 2y + sina 1+2 1 +...
Va2 y da dy The region A is bounded by the curve: 2+y=Va 3. Evaluate C 2102 dz dy dz 4. Evaluate The solid V bounde...
Va2 y da dy The region A is bounded by the curve: 2+y=Va 3. Evaluate C 2102 dz dy dz 4. Evaluate The solid V bounded by surfaces: z = 1-2, z = y , y = 0
Va2 y da dy The region A is bounded by the curve: 2+y=Va 3. Evaluate C 2102 dz dy dz 4. Evaluate The solid V bounded by surfaces: z = 1-2, z = y , y = 0
Problem 1: A) Evaluate the iterated integral. A1) S S**** S*yz dy dz dx Ans: A2)...
Problem 1: A) Evaluate the iterated integral. A1) S S**** S*yz dy dz dx Ans: A2) SS, (x + 2y) dV, where E is bounded by the parabolic cylinder y - xand the planes x -2, x = y, and z o Ans: And
please check your answer Question Details Let W be the solid in the first octant bounded by the top half of the cyl...
please check your answer
Question Details Let W be the solid in the first octant bounded by the top half of the cylinder x2 +z2= 36 and the plane x + y = 6 y Use Cartesian (rectangular) coordinates to set up the integral to find the volume of W in the order dydxdz. dy dz dx For instructor's notes only. Do not write in the box below.
Question Details Let W be the solid in the first octant bounded...
must be in the order of dx dy dz 2. ONLY Find the limits when DV...
must be in the order of dx dy dz
2. ONLY Find the limits when DV is written as dx dy dz (the integration has to be done in this order). SSS, f (x,y,z)dV where f(x, y, z) = 1 – x and D is the solid that lies in the first octant and below the plane 3x + 2y + z = 6.
All of 10 questions, please. 1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the...
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
2 147 a. Evaluate the triple integral (convert to oylindrical)12I, J xz dz dx dy b. Find the mome...
2 147 a. Evaluate the triple integral (convert to oylindrical)12I, J xz dz dx dy b. Find the moment of inertia about the z-axis for the solid in the first octant bounded by x2+y2 -4 and z2-x2 + y2 if the density is given by: z. (Use cylindrical.) c. Find the mass of the solid bounded by z2 -x2 +y2 and z 1 in the first octant, if the density is given by: cos. (Use spherical.)
2 147 a. Evaluate...
11. Evaluate S. 'S*(1 + 3x2 + 2y?) dx dy. 12. Find the volume in the...
11. Evaluate S. 'S*(1 + 3x2 + 2y?) dx dy. 12. Find the volume in the first octant of the solid bounded by the cylinder y2 + z2 = 4 and the plane x = 2y. Graph for Problem 12 13. Find the volume under the paraboloid z = 4 - x2 - y2 and above the xy-plane. N Consider the solid region bounded above by the sphere x + y + z = 8 and bounded below by the...
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,...
Question 11 A solid in the first octant, bounded by the coordinate planes, the plane (x= a) and the curve (z=1-y). Find the volume of the solid by using : #-Double integration technique (Use order dy dx) a=51 b-Triple integration technique (Use order dz dy dx) ..
10) Calculate the integral zdac dy dz where D is bounded by the planes x = - 0, y = 0, z = 0, z = 1, and the cylinder x2 + y2 = 1 with x > 0 and y> 0. 11) Let y be the boundary of the rectangle with sides x = 1, y = 2, x = 3 and y = 3. Use Green's theorem to evaluate the following integral 2y + sina 1+2 1 +...
Va2 y da dy The region A is bounded by the curve: 2+y=Va 3. Evaluate C 2102 dz dy dz 4. Evaluate The solid V bounded by surfaces: z = 1-2, z = y , y = 0
Va2 y da dy The region A is bounded by the curve: 2+y=Va 3. Evaluate C 2102 dz dy dz 4. Evaluate The solid V bounded by surfaces: z = 1-2, z = y , y = 0
Problem 1: A) Evaluate the iterated integral. A1) S S**** S*yz dy dz dx Ans: A2) SS, (x + 2y) dV, where E is bounded by the parabolic cylinder y - xand the planes x -2, x = y, and z o Ans: And
please check your answer
Question Details Let W be the solid in the first octant bounded by the top half of the cylinder x2 +z2= 36 and the plane x + y = 6 y Use Cartesian (rectangular) coordinates to set up the integral to find the volume of W in the order dydxdz. dy dz dx For instructor's notes only. Do not write in the box below.
Question Details Let W be the solid in the first octant bounded...
must be in the order of dx dy dz
2. ONLY Find the limits when DV is written as dx dy dz (the integration has to be done in this order). SSS, f (x,y,z)dV where f(x, y, z) = 1 – x and D is the solid that lies in the first octant and below the plane 3x + 2y + z = 6.
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
2 147 a. Evaluate the triple integral (convert to oylindrical)12I, J xz dz dx dy b. Find the moment of inertia about the z-axis for the solid in the first octant bounded by x2+y2 -4 and z2-x2 + y2 if the density is given by: z. (Use cylindrical.) c. Find the mass of the solid bounded by z2 -x2 +y2 and z 1 in the first octant, if the density is given by: cos. (Use spherical.)
2 147 a. Evaluate...
11. Evaluate S. 'S*(1 + 3x2 + 2y?) dx dy. 12. Find the volume in the first octant of the solid bounded by the cylinder y2 + z2 = 4 and the plane x = 2y. Graph for Problem 12 13. Find the volume under the paraboloid z = 4 - x2 - y2 and above the xy-plane. N Consider the solid region bounded above by the sphere x + y + z = 8 and bounded below by the...
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