A solid is obtained by rotating the shaded region about the specified line. about the x-axis y 4| 3 2 y = Vx 1 y = 6– x 2 4 6 8 10 (a) Set up an integral using the method of cylindrical shells for the volume of the solid. V = + 6 - y 2пу dy (b) Evaluate the integral to find the volume of the solid. 80л 3

Q: Use a triple integral to find the volume of the solid shown in the figure. z = 36 - x2 - y2 40 30 20…

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Q: se the method of cylindrical shells to find the volume V of the solid obtained by rotating the…

A: Use the method of cylindrical shells to find the volume 'v' of the solid by rotating the region…

Q: The volume of the solid obtained by rotating the region bounded by 2y', y = 1, x = 0, about the…

A: Given

Q: d by revolving the area enclosed by: x = y2 +1 , x = 0, y = 0 and y = 2 about: y = 2

A: Introduction: The formula of shell method using the horizontal axis of revolution is given by,…

Q: The volume of the solid obtained by rotating the region bounded by y = x², y = 5x, about the line x…

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Q: A spherical tank of diameter 6 m is full of water. Set-up the integral for the work done in pumping…

A:

Q: A solid is obtained by rotating the shaded region about the specified line. about the x-axis y 4| y…

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Q: A solid is obtained by rotating the shaded region about the specified line. about the x-axis y 4 3 y…

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Q: Use a double integral to find the volume of the indicated solid. 8 z = 8- X- y 6. 4 1 2 4 V 3 y=4 4…

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Q: Use a double integral to find the volume of the indicated solid. 16 15 z = 16 - x - y 14 13 12 11 10…

A: Volume of the solid using, double integrals

Q: Express by repeated integrals, the volume of the solid bounded above by the plane 2x + 2y -z +1= 0,…

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Q: Use a double integral to find the volume of the indicated solid. 8. z = 8- X - y 6. 4. 3 2 1 1 1 2.…

A: We need to find volume.

Q: The volume of the solid obtained by rotating the region enclosed by y = x°, y = 36x, x >0 about the…

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Q: Use a double integral to find the volume of the indicated solid. 8 z = 8-2y y y=2 X 4. X=4 2)

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Q: Use a triple integral to find the volume of the solid shown in the figure. z = 16 - x2 - y2 130 10…

A:

Q: The volume of the solid obtained by rotating the region bounded by y = x², = 2x, about the line x =…

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Q: The volume of the solid obtained by rotating the region enclosed by y = 3 24х — 3х-, у%3D0 about the…

A: We first sketch the region using a graphing calculator  The shaded region is rotating about the y…

Q: dn the integral for the volume of the solid obtained by rotating the region bounded by Set y = 2+…

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Q: Use a triple integral to find the volume of the solid bounded by the graphs of the following…

A: Use a triple integral to find the volume of the solid bounded by the graphs of the following…

Q: What is the volume of the solid formed by revolving the region bounded by the graphs of x2 = 9y and…

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Q: 3- By using the disk method, determine the integral which gives the volume of the solid obtained by…

A: Therefore, the X-axis and X=3 and y=e-x has the radius of r=e-x-3.

Q: A solid is obtained by rotating the shaded region about the specified line. about the x-axis y 2 y =…

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Q: Express by repeated integrals, the volume of the solid bounded above by the plane 2.x + 2y - +1= 0,…

A: The given question is solved below.

Q: The volume of the solid obtained by rotating the region bounded by y = x?, y = 4x, about the line a…

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Q: Use the shell method to set up and evaluate the integral that gives the volume of the solid…

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Q: Which of the following is the integral equivalent of the volume of the solid formed by rotating…

A: First obtain the points of intersection x2-3=3x+1x2-3x-4=0(x+1)(x-4)=0x=-1,4y=-2,13 Intersection…

Q: A solid is obtained by rotating the shaded region about the specified line. about the x-axis y= 20…

A: Given that, the two curves are y=x and y=20-x. y=x and y=20-xy2=x and x=20-y Obtain the limit of the…

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

A: The limits of : y is from 0 to 6 x is from 0 to 6 z is from 0 to 2xy.

Q: Use the method of cylinders to determine the volume of the solid obtained by rotating the region…

A: We first sketch the region using a graphing calculator.

Q: A solid is obtained by rotating the shaded region about the specified line. about the y-axis y y = 4…

A: We need to find the volume of the solid formed by rotation.

Q: Use a triple integral to find the volume of the solid shown in the figure. z 64 x2-y2 20 60 50 40 30…

A: Given equation of the solid: z=64-x2-y2 Aim: to find the volume of the solid  Method used: triple…

Q: A spherical tank of diameter 6 m is full of water. Set-up the integral for the work done in pumping…

A:

Q: What is the volume of the solid formed by revolving the region bounded by 8y = r? and 8z = x axis? 7…

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Q: Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the…

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Q: Use a double integral to find the volume of the indicated solid. 8 z = 8- x - y 7 4 1 1 4 V 3 y=4 4…

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Q: 2) 2. Use a double integral to find the volume of the indicated solid. 4. z = 4 – X – y 31 y=2 X=6

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Q: Use a double integral to find the volume of the indicated solid. 8 z = 8- X- y 4 21 4. y-4 4. y=x 3.…

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Q: To calculate the volume of the solid region between the spheres  x2 + y2 +z2 = 1 and x2 + y2 + z2 =…

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Q: 2- By using the disk method, determine the integral which gives the volume of the solid obtained by…

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Q: Use a double integral to find the volume of the indicated solid. 12 z = 12 – x- y 11 10 8 7 5 4 2 1…

A: The expression for the volume as double integral is: V=∬zx,ydydx Given: z=12-x-y   From the given…

Q: Consider x^2 + y^2 = 12, x^2 + y^2= 3 and z = 5 in the first octant. a. SET UP the Cartesian triple…

A: A cartesian coordinate system contains three mutually perpendicular number lines named x axis, y…

Q: Use a triple integral to find the volume of the solid shown in the figure. z = 16 – x2 - y² 130 10…

A: Let's find.

Q: Use a double integral to find the volume of the indicated solid. 16 15 z 16- X-y 14

A: We are given the following. So, we have 0≤z≤16-x-y,  x≤y≤8, 0≤x≤8.

Q: Find the volume of the solid generated by revolving the region bounded by y= 3x, y= 0, and x = 3…

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Q: Use a triple integral to find the volume of the solid shown in the figure. z = 16 - x2 - y2 120 10…

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Q: The volume of the solid obtained by rotating the region enclosed by y = 14x – 2x, y = 0 about the…

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Q: Which of the following integrals gives the volume of the solid generated by rotating region enclosed…

A: we have to use washer method for finding volume around x-axis

Q: The volume of the solid obtained by rotating the region enclosed by y = 1/x°, y = 0, x = 1, r = 4…

A: Volume is the amount of space inside any solid. When an area is rotated about any fixed axis, then…

Q: Express by repeated integrals, the volume of the solid bounded sbove by +2y-+1-0, on the sides by…

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Q: Use a triple integral to find the volume of the solid shown in the figure. z = 16 – x2 - y2 130 10…

A: