Evaluate the given integral over the solid ellipsoid n uvw-space.) SSS 7 xyz/dxdydz D -≤9. (Hint: Let x = au, y = bv, and z = cw. Then integrate over an appropriate region

Q: fof 8 6 5 1 3 2 5.6 8 9 10 1 Find the centroid of the region displayed in the graph. (x, y) =

A: We have to find the centroid of the shaded region:

Q: on given by E.

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Q: Evaluate the surface integral JSF dS where F = (5x, 3z, -3y) and S is the part of the sphere a² +…

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Q: Evaluate the triple integral using only geometric interpretation and symmetry. G (7 + 5x²yz²) dv,…

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Q: Find the centroid of the region bounded by the given curves. y = 6 sin 5x, y = 6 cos 5x, x = 0, x =…

A: According to the given information it is required to calculate the centroid of the region bounded by…

Q: Evaluate the triple integral. JJJ 8x dV, where E is bounded by the paraboloid x = 5y² + 5z² and the…

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Q: Evaluate the triple integral. 4x dV, where E is bounded by the paraboloid x = 5y2 + 5z2 and the…

A: We have a paraboloid, and each cross section is a circle, parallel to the plane x = 5. We use…

Q: .4 7 [T 4 Find (x + y) dydx.

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Q: Evaluate the triple integral (* + 1y) dV where E is bounded by the parabolic cylinder y = 32² and…

A: We have to find the triple integral  ∫∫∫E(x+y)dVwhere E is bounded by the parabolic cylinder y=3x2…

Q: 1 = √√√₁₂² xy dA, where D is the triangular region with vertices (0, 0), (6, 0), (0, 1). Evaluate…

A: To Evaluate: I=∬Dxy dA where the D is the triangular region with vertices (0,0), (6,0), and (0,1).

Q: a y = h an xn h X Locate the centroid of the area. Express your answer in terms of some or all of…

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Q: Evaluate the triple integral. [[[ 8x² dV, where T is the solid tetrahedron with verticies (0, 0, 0),…

A: Given that: The integral is ∫∫∫T8x2dv. The vertices are (0,0,0),(1,0,0),(0,1,0),(0,0,1). The…