What is the center of gravity of the solid formed when the plane region bounded by y = x, y = 2x, and x + y = 6 is revolved about the y-axis ? O (13/5,0) O (3/5,0) 2 O (0, 13/5) O (0,3/5) O NA

Q: Use spherical coordinates to evaluate x² + y² + z² = 36. I x² + y² dV, where E is the region between…

A: is the region between the spheres and .We have to find .

Q: || (2? + y*) cos(zy) dz dy? R

A: Here the Cartesian coordinates (x,y) are converted into (u,v) by substitution method as xy=u, x2-y2…

Q: 1. Locate the centroid of the given areas. y ·b 06 PROB 05-06 (a) X 1 m 06 PROB 09-10 (b) =0.5e² y=…

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Q: x dV

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Q: b) Given F(r, y, z) = (x³ + cosh z) i+ (2y - 3ry)j – (x² + 4y²z) k. Use %3D Gauss's theorem to…

A: 1. The divergence is an operator, which takes in the vector-valued function defining this vector…

Q: Use spherical coordinates to find [[[, z2 dV.

A: In this question, we find the triple integral by using spherical coordinate with a sketch of solids

Q: Use Cartesian coordinates to evaluate [[[ ²² y² dv D where D is the tetrahedron in the first octant…

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Q: O Evaluate 2 fff ( x + y ) dv G where G is a solid took thes to sicle bounded by the parabolic…

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Q: Use cylindrical coordinates to calculate w f(x, y, z) dV for f(x, y, z) = x, x² + y 0, y > 0, and…

A: To evaluate ∫∫∫Wfx,y,zdV, Where fx,y,z=x  & W is the region bounded by x2+y2≤9,x≥0,y≥0…

Q: III Find the area of the portion of the cylindrical surface y = 4- a2 in the first octant that is…

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Q: Use cylindrical coordinates to calculate Jw J(x, y, z) dv for f(x, y, z) = x, (Use symbolic notation…

A: To evaluate ∫∫∫Wfx,y,zdV, Where fx,y,z=x  & W is the region bounded by x2+y2≤9,x≥0,y≥0…

Q: 2. Let W be the region where x2 + y? + z2 2. Use spherical coordinates to find I (2? + y? + 2?)-i…

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Q: Let S be the solid obtained by rotating the region bounded by C1: y = x2 − 6x + 9 = (x − 3)2 and C2:…

A: The given curves are y=x-32, and y=x+3. To Sketch: The region bounded by the above curves and which…

Q: Evaluate TI Vx + y2 dv, where E is the region that lies inside the cylinder x2 + y? = 1 and between…

A: In this question, we have to evaluate the triple integral by using cylindrical coordinates.

Q: ch is the centroid of the section reckoned lower left hand corner. 100 100 600 100 -500- Dim

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Q: b) Given F(x, y, z) = (x³ + cosh z) i+(2y³ – 3x²y) j – (x² + 4y²z) k. Use Gauss's theorem to…

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Q: Evaluate || F.ndS F = xi + yj+(z² –1)k if and o is the curved surface of the cylinder y = \4-x? from…

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Q: JJ F- ndS if F= xi + yj+(z² –1)k Evaluate and o is the curved surface of the cylinder y = V4-x? from…

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Q: Let o(r, y, 2) = x2 + (y/2)2 + 22. Find the point on the ellipsoid o = 1 closest to (1, 1, -1).

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Q: w √√x² + y² dv, where W is the region between the half cone zwx+yeyers, and ircular paraboloid z=2-…

A: A volume integral is given over the region W. The aim is to find the volume integral for the given…