If, in an integral triple, we have a D region bounded by the surfaces z = 2x² - y² and z = 9 - 2x² + 2y², what are the limits of integration with respect to z?

Q: The volume generated when the region bounded by y = x, y = 1, x = 0 is rotated about x axis is -

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Q: Compute volume under the surface x+ 2y2 above the region described by 0sxs1 and 0sysx?, shown below.…

A: Given that surface is x+2y2 and region is described by 0≤x≤1 and 0≤y≤x2. It is required to find the…

Q: write the triple integral for integrating f(x,y,z) over the region in the first octant bounded above…

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Q: 5xcos(y)dA, D is bounded by y=0, y=x2 ,x=9

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Q: Set up a double integral that gives the volume of the region bounded by the two paraboloids z = x2 +…

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Q: 2y Calculate the double integral in a general region where z = x² +1 0, x= 1, y = 0, y = √√x bounded…

A: Since you have posted multiple questions, we will solve the first question for you. If you want any…

Q: 1 -drdydz JSJ (x² + y² + 22)#

A: Use spherical coordinate system to solve it.

Q: Suppose that f(x, y) = x + 7y and the region Dis given by {(x, y) | – 4 < x < 3, – 4 < y < 3}. D…

A: Perform double integral as show...

Q: Choose five other iterated integrals that are equal to the given iterated integral. f(x, y, z) dz dy…

A: Given iterated integral,

Q: Use a triple integral to find the volume of the solid bounded by the graphs of the equations. z =…

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Q: Sketch the region R whose area is given by the iterated integral. dx dy 1.5 1.5 0.5 0.5 -0.5 0.5 1.5…

A: Firstly, we can draw the graph and after that we  can change iterated integral.

Q: The volume of a solid is described by the double integral L 3 x’y dydx If the order of the integral…

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Q: The area bounded by y=3Vx and 2y= 3x is revolved about the x-axis. Using cylindrical shell method,…

A: Using cylindrical shell method.

Q: The volume of the solid obtained by rotating the region enclosed by y = x", y = 6x, about the line y…

A: First sketch the curves then use method of disc to get the volume of solid obtained.

Q: Find the volume of the solid generated by revolving the area bounded by x2 – 2kx – 3ky + k² = 0 and…

A: Given curves are:  x2-2kx-3ky+k2=0 3x-3y+k=0 The area bounded by them is revolving about the line…

Q: Set up an integral to find the volume of the solid generated when the region bounded by y = VT and y…

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Q: Suppose that f(x, y) = 2x + 3y and the region D is given by {(x, y) | −1≤ x ≤ 5, − 1 ≤ y ≤ 5}. D…

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Q: Use an iterated integral to find the area of the region bounded by 2x - 5y=0, x+y=6, y=0.

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Q: Calculate the double integral ∬Rdxdy, where the region R is bounded by the parabolas y2=2x, y2=3x…

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Q: Suppose that f(x, y) = x + 6y and the region D is given by {(x, y)| – 3 < x < 3, – 3 < y < 3}. - D…

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Q: Sketch the region R whose area is given by the iterated integral. * 64 – y² dx dy 60- 50- 40- 30- 20…

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Q: Consider calculating the size of the region N:= {(x, y) E R² : y > v3x², æ² + y² < 4} , with the 2d…

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Q: Find the volume of the 'ice-cream' that is bounded by x2 + y2 + z2 = 51 and the upper cone z2 = 3x2…

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Q: Find the volume of the solid generated by revolving the area bounded by x2 – 2kx – 4ky + k2 = 0 and…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Suppose that f(x, y) = 4x + 2y over the region D = {(x, y) | 1 < ¤ < 2, x² < y < 4}. D Then the…

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Q: Calculate f 4y dydx, Where R is a region bounded by y=x* and y= - 3x2 - 2

A: Given integral is ∬R4ydydx, where R is a region bounded by the curve y=x2 and y=−3x2−2. We have to…

Q: Suppose that f(x, y) = 8x + 4y and the region D is given by {(x, y) | –1< x < 1, – 1 <y< 1}. D Then…

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Q: Given a solid bounded by f(x,y) = 3x² + 2y“, xy-plane, x = 3, x = 12, y = 6 and y = 16. If the order…

A: find the volume using double integration.

Q: Integrate f(x, y, z) = x over the region in the first octant bounded above by z = 8 - 2x 2 - y2 and…

A: Given that, z=8-2x2-y2        ...(1)z=y2              ...(2)

Q: Set up the double (dydx) and triple (dzdxdy) iterated integral that will solve the volume of the…

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Q: Given a solid bounded by f (x, y) = 5x2 + 4y", xy-plane, x = 4, x = 9, y= 5 and y = 15. If the order…

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Q: Let S be the solid in the first octant bounded by the cylinders x² +y² = 4 and x² + z² : -) Use…

A: The volume of the given solid S is V=∫∫∫S dVwhere solid is bounded by cylinders x2+y2=4 and…

Q: The volume of the solid obtained by rotating the region enclosed by y = x², y = 3x, about the line y…

A: Given: y=x2 ; y=3x   Now find the point of intersection between the curve and line;…

Q: Sketch the region R whose area is given by the iterated integral. 8 (64 - y2 dx dy 60 8. 50- 6- y 4…

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Q: Set up the double integral that will find the volume of a solid bounded by z = 1-y²-2² and the ry-…

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Q: Suppose that f(x, y) = 5x + 3y and the region D is given by {(x, y) | - 3 < x < 3, – 3 < y < 3}. D…

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Q: Evaluate the double integral S, x dx dy where the region R is bounded by: R 9. y = 4x – 3, y =x +, y…

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Q: Find the volume of the solid generated by revolving the area bounded by x² – 2kx – 3ky + k² = 0 and…

A: Given curves are:  x2-2kx-3ky+k2=0 3x-3y+k=0 The area bounded by them is revolving about the line…

Q: ydV, E

A: We will draw a region first, then will find limits

Q: Sketch the region R whose area is given by the iterated integral. r 64 - y2 Хр хр 6 4 6 2 4 10 20 30…

A: Given integration is, ∫-88∫064-y2dxdy The region of integration is bounded by, x=0, x=64-y2, y=-8,…

Q: Set up the double integral that solves for the volume of the solid bounded by the cylinder x² + y? =…

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Q: What is the integral of f (x, y, z) = 4 y2 + 5 y z over the region bounded by –12 x +8 y – 2 z= -38,…

A: We will find out the required value of integral.

Q: The area bounded I led by y=3x and 2y=3x is revolved about the y-axis. Using circular ring method,…

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Q: Use an iterated integral to find the area of the region bounded by 2x - 5y = 0, x+y=6, y = 0.

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Q: The area bounded by y=3x and 2y=x is revolved about the x-axis. Using cylindrical shell method, set…

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Q: The area bounded by y=3Vx and 2y=3x is revolved about the y-axis. Using circular ring method, set up…

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Q: Sketch the region R bounded below by the curve y = x², on the left by the line x = 1 and above by…

A: The region bounded by the curves is as below:

Q: Suppose that f(x, y) = 6x + 2y and the region D is given by {(x, y) | - 5< x < 3, – 5 < y < 3}. D…

A: Given fx,y=6x+2y and Region D= x,y: -5≤x≤3, -5≤y≤3 Now…

Q: Sketch and set up the integrals for volume of the region bounded by y = x^2 + x - 2 and y = 3x + 13,…

A: Given are the curves  y=x2+x-2 and y=3x+13 We need to set up the integral for the volume of the…

Q: The area bounded by y=3Vx and 2y=3x is revolved about the y-axis. Using circular ring method, set up…

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