Evaluate the triple integral. 8z dv, where E is bounded by the cylinder y2 + z2 = 9 and the planes x = 0, y = 3x, and z = 0 in the first octant

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Q: (b) Find the value of the following integrals: z-1 1- dz, y is the triangle with vertices at the…

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Q: evaluate the triple integral. where T is the solid tetrahedron with vertices (0, 0, 0), (1, 0, 0),…

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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: Exer.) Express and evaluate the integral (x+y) dv E as an iterated integral for the given solid…

A: Given:

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Q: 3 3y Evaluate the iterated integral ry de dy.

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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…

Q: Evaluate the triple integral.  (x2 + y2) dx dy dz; W is the pyramid with top vertex at (0, 0, 2)…

A: The given triple integral is,

Q: Evaluate the triple integral.   3xyz dV, where T is the solid tetrahedron with vertices (0, 0, 0),…

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Q: Locate the centroid x of the shaded area. y = h xn h X

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Q: 3 1 4 1 | |(2x – 4y)dydx (2х — |x²ydxdy 3. 4. - 1 2 0 2π π |(sinx + cosy)dxdy 5.

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Q: Q.2) Find the centroid of the plane area shown below using integration. y y²= 3x y = x²/3 X

A: Given: y2=3x and y=x23 To find the centroid of the plane area  The formula for the centroid of…

Q: P. 2. Evaluate the triple integral S' L___7z S"'¹m(1 + √2² + y² + z2²)dzdydr. 0

A: Consider the integral as The objective is to evaluate.

Q: Evaluate the integrally.dy.W 6y+ 34

A: To evaluate