Each of the definite integrals in Exercises 11–16 represents the volume of a solid of revolution obtained by rotating a re- gion around either the x- or y-axis, computed with the shell method. Find this region. a/4 -1 x cosx dx | x(x³) dx 11. 27 12. 27 0. r5 13. 27 | yvy - 4 dy 14. 27 | (x? – x³) dx 0. 1 15. 27 | y lny dy 16. 27 | (3y – 3y?) dy

Q: Given If G is the solid bounded byz =6-y, z=y-10 and y=x2 where dV = dzdydr. Find the lower and…

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Q: 22 Use a triple integral to find the volume of the given solid. The solid enclosed by the evlinder…

A: According to question,Given Cylinder and planes,x2 + z2 = 4y = -1y+z = 4

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A: We need to set up integral.

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Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

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Q: Define R as the region bounded by the graphs of f(x) = 3√x and g(x) = over the interval [1, 3].…

A: Given thatRegion bounded by y=x28 , y=3xx=1 and x=3Using cylindrical shell mathod…

Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

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Q: A solid is generated by revolving the area in the first quadrant bounded by y = , its asymptotes and…

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Q: In Exercises 17-22, iterated integrals are given that compute the area of a region R in the x-y…

A: We have to find as given above.

Q: Evaluate the integral (x + z) dS where S is the part of the cylinder y + z2 = 4 with x E [0, 9].

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Q: Evaluate the following integral: | VE sin(2t3/2) dt b) Use the shell method to find the volumes of…

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A: Given  we have to find the integral ∫∫Ω 2y dydx

Q: Which of the following integrals represents the volume of the solid of revolution formed by…

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Q: Let E be the solid region in the first octant bounded by the coordinate planes, the cylinder x2 + y2…

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Q: The double integral Jf 2xycosydA over the rectangular region R= {(x, y) E R2, 0<x<1 and 0 < y<n} is…

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Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

A: Please see the below picture for detailed solution.

Q: Find by double integration the volume of the finite solid lying underneath the graph f(x, y) = x² –…

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Q: The value of the triple integral II| 2x² dV where E is the region inside both x? + y? + z? = 36 and…

A: Solution:-

Q: 1. Evaluate the given integral Q. -L LL²³ . = (2x − z) dz dy dx Зг 2. Give the (upper, lower,…

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A: Let's find.

Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

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Q: Set up the integral used to compute the mass of the solid in the first octant enclosed by r = 3…

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Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

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Q: The region under the curve y = x2 x between 1 and x 3 is revolved about the line x = 3. Using the…

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Q: 5. Let S be the solid in the first octant bounded by the cylinders x² + y? = 4 and x² + z² = 4. (b)…

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A: The region In XY-plane  (Or down side view)

Q: #2. Evaluate the triple integral x dV, E where E is given by E = {(x, y,z) : z< x < 2z, 0 < y<x+z,…

A: Solve it

Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

A: Given:      fx=x-13       gx=x-1 Volume of solid generated by revolving around the region is…

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A: evaluate the triple integral ∫∫∫Ez dV where E is bounded by the cylinder y2+z2=9 and the planes x=0…

Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

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Q: (0,2) y =v4-x A (4,0) Which of the following double integrals has bounds that represents the region…

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Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

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Q: The double integral ff 2xy³dA over the rectangular region R = {(x, y) E R², 0<x<4 and–1<y<0}is equal…

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Q: The volume of the solid E bounded by the cylinder x + y² = 1, and the planes z = 1 and z = 3 in the…

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Q: Which of the following integrals represents the volume of the solid obtained by rotating the region…

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Q: Verify Green's Theorem by evaluating both integrals ƏN Ly? dx + x² dy dA ду - %D ax For the given…

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Q: Consider the region in the first quadrant, bounded by the curves y=x^3, y=x^(1/2). For each of the…

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