Use spherical coordinates to evaluate 3 √9-x² 9-x²-y² x² + y² + z² 1 + (x² + y² + z²)² Hint: Draw the volume of integration in (x, y, z) space to determine what the bounds are in (p, 0, 0) space. dzdydx.

Q: Find the volume of the solid bounded by the paraboloids z = −4+2x² + 2y² and z = 3 - 2x² - 2y²

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Q: Use divergence theorem to find the volume of quadric surface z² + 3y + 4x² = 3 with the solid region…

A: Given F→=xzi^+3yzj^+x2k^. We have to find the volume of quadric surface z2+3y+4x2=3 with the solid…

Q: The region bounded by y = v9– x² and y = 0 has an area of . Find the y-coordinate of its centroid.

A: Suppose the region is bounded by fx and gx on a,b where fx≥gx .Assume centroid is denoted by x¯,y¯…

Q: Compute the volume of D = {(x, y, z): x² + y² < z < 2y, x² + (y - 1)² < 1}.

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Q: s(x) = - (x – 8)(x – 15) 20 - g(x) = - + 30 (10,15) 15 (10, 15), V Label • (14,9) V Label | (14, 9).…

A: (a.) Given: A 3D solid whose base is T is formed from the intersection of f and g. It has…

Q: Q5) Find volume of body bounded by z2 + y2 + x2 = 4.

A: Given equation is z2 + y2 + x2 = 4

Q: Find the volume of the solid V in the first octant bounded by x + y + z = 5 and x + y + 4z = 5. (Use…

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Q: 5) Consider the parallelogram with vertices (0,0), (4,0), (6,2) & (2, 2). We know the area of this…

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Q: Find the volume of the 'ice-cream' that is bounded by x2 + y2 + z2 = 95 and the upper cone z2 = 4x2…

A: We have to find the volume of the 'ice-cream' that is bounded by x2 + y2 + z2 = 95 and the upper…

Q: Q1) Find plane area bounded by y = 2,y = 6 – x, and y = 8 - 3x using double %3D

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Q: Evaluate the double integral  SSDxydA where D is the triangular region with the vertices (0,0)…

A: ∬DxydA, where D is triangular region with vertices (0,0), (3,0) and (0,1).

Q: Find the area +6 C1 R -6 +6 C2: 4x2 + y² = 16 -6 using green's theorem.

A: We are given the above region of which we need to find the area and as per the instruction, we need…

Q: y=2x-x² and y+3=0

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Q: Q5) Find volume of body bounded by z² + y² + x² = 9.

A: Explanation of the answer is as follows

Q: 5. Sketch the solid in the first octant that is bounded by the graphs of 22 +22= 9, y = 2x, y = 0…

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Q: Find the integral of the function f (x, y) = x°y on the triangular plane region whose vertices are…

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Q: Determine the volume of the function f(r, 0, z) = -2r²0z³ in a complete cylinder of radius 3 and…

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Q: Express frydA, where R is the triangular region with vertices (0, 0), (3, 1) and (-2, 1), as an…

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Q: Evaluate the integral (3x +y)dA {(x,y)|-2sy53, y -35xsy+3}.

A: It is asked to evaluate the integral, the region D is defined as, D = {(x,y) | -2 ≤ y ≤ 3,  y2-3 ≤…

Q: What is the volume of the figure between the planes z = x + y and z directly above the rectangle…

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Q: Use calculus to show that the maximum possible area of a triangle with one vertex at (0, 0) and the…

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Q: Consider the sequence defined by a_n= (4n + (-1)^n2 - 2)/8 for every integer n > 0. Find an…

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