The region bounded by y = a x², x = 1, and y = 0 in quadrant I is rotated around z - axis. Given that the volume of the solid generated by this revolution is -T, find the value of a. 4 1 10 25 25 4. 1/2 b)

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A: Consider the provided question, The base of a solid is the region between the curve, y27+x=x221-x,…

Q: The region bounded by y = a x, a = = 1, and y 0 in quadrant I is rotated around %3D - axis. Given…

A: In the question it is asked to calculate the value of a ,volume generated by the curve y=ax2 is…

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Q: The region bounded by y = 0 and y = kx – x is revolved around the y-axis to form a solic whose…

A: Given,        y=0, and  y=kx-x2

Q: Find the volume that is obtained by revolving the region about the r-axi 20 18+ 16+ 14+ 12+ 10+ y =…

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Q: 1. Find the volume of the solid generated by revolving the region in the first quadrant bounded by…

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Q: The base of a solid is the region between the curve, y?(p + x) = x²(3p – x), 0 < x < 3p,y 2 0 and…

A: The solution is given below

Q: Find the volume of the resulting solid if the region under the curve 6 y = 2 x + 3x + 2 from x = 0…

A: To the  find volume.

Q: . The region bounded by y =x°, y= 0, and x = 2 is revolved about the line X=2. Find the volume of…

A: Let us first plot the required region.

Q: The base of a solid is the region between the curve, y (p + x) = x²(3p – x), 0 0 and the X – axis.…

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Q: If you rotate the region bound by y = fx,x = h, y = 0 about the x-axis, you obtain a right- circular…

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Q: The region bounded by y = ca, a = 1 and the r-axis in quadrant I, is rotated 257 around the x-axis,…

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Q: The region under the curve y = tan? x from 0 to T/4 is rotated about the x-axis. Find the volume of…

A: Given data: *The equation of the curve is y=tan2x *The curve is rotated from 0 to π4 about the x…

Q: Find the exact volume of the solid formed when the region bounded in Quadrant I by the axes and the…

A: The volume of a solid formed by revolving the region bounded by the curve y=f(x) and the x axis is…

Q: O Find the volume of revolution (either by shells or Liashers) when the region enclosed bu by…

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Q: Find the volume of the region common to the interiors of the cylinders x2 + y = 1 and x? +z? = 1,…

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Q: The base of a solid is the region between the curve, y?(p + x) = x²(3p – x),0 0 and the X – axis.…

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Q: The region bounded by y = cx , x = 1 and thex-axis in quadrant I, is rotated around the x-axis, and…

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Q: b) Find the volume of the solid which is in the first octant and bounded between the spheres p = 1…

A: To find- Find the volume of the solid which is in the first octant and bounded between the spheres ρ…

Q: raph on the image below and find the volume generated by revolving the area bounded by 9x^2 + 4y^2 =…

A: We need to find volume.

Q: Find the volume of the solid formed by revolving the region bounded by the graphs y=x and y=x? from…

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Q: ind the volume of the solid generated by revolving the region in the first quadrant bounded by the…

A: Given problem:- Find the volume of the solid generated by revolving the region in the first quadrant…

Q: Find the volume of the solid that results when the region enclosed by x = 0, x = 9, and y: 0 is…

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Q: Find the positive constant A given that the volume of the solid bounded by the paraboloid, x2 + y2…

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Q: 31 Find the volume of the solid generated by rotating the shaded region R through 360° about the…

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Q: The region enclosed by y=2Vx and y=6 is revolved about the x-axis. The volume of the solid generated…

A: The given curves are: y=2x, y=6

Q: Refer to the figure and find the volume generated by rotating the given region about the specified…

A: Given data:     The given function is: y=2(x)1/4. The given limits of y is: [a,b]=[0,2].   The given…

Q: What is the volume in cubic units of the solid formed when the region bounded by y = 2x + 1, x-axis,…

A: Given :y=2x + 1, x- axis, x=1, and x=2 is revolved about y=0.Formula :Volume in cubic = π∫y2 dy

Q: What is the volume in cubic units of the solid formed when the region bounded by y = 3x - x^3,…

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Q: 1. Use the cylindrical shells to find the volume of the solids generated when the shaded area is…

A: The volume of solid of revolution can be calculated using the cylindrical elements. The formula for…

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Q: Find the volume of the solid that lies under the cone z = x² + y² and above the annulus 4 < x² + y?…

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Q: What is the volume, in cubic units, of the rotating object formed by rotating the y = v9 – x2 curve…

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Q: D Evaluate the volume of the solid region E, in the first octant, that lies above z0 and below the…

A: Explanation of the answer is as follows

Q: d the volume of the solid whose base is the region enclosed by y = x² and y = 2, and the cross…

A: Topic:- application of integration

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Q: Compute the volume of the solid above the cone o = , and between the spheres p = 1 and p = 3. Hint:…

A: We have to use spherical co ordinate system

Q: A region bounded by f(x) = 3x + 1, y = 3, x = 1, and x = 2 is shown below. %3D Find the volume of…

A: Given :-  The region bounded by f x  = 3x + 1 , y = 3 , x = 1 , x = 2 To Determine :-  The volume of…

Q: Find the volume of the solid generated when the region enclosed by y = a, x = 1 and y O is revolved…

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Q: 31 Find the volume of the solid generated by rotating the shaded region R through 360° about the…

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Q: Graph on the image below and find the volume generated of the area bounded by x^2 = ay, the x-axis…

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Q: The volume of the solid generated by revolving the region bounded by x²=4y and y2=4x about y=4 is to…

A: Option (A) is correct.

Q: 5. For the right circular cylinder, suppose that r = 5 in. and h = 6 in. Find the exact and…

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Q: A volume is described as follows: 1. the base is the region bounded by æ = - y? + 10y + 95 and æ =…

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Q: Find the volume of the solid generated by revolving the specified region about the given line. R…

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A: To find the volume of solid rotating about y axis.

Q: A) Find the volume of the solid that is bounded below by the hemispherep = 1, z>0 and above by the…

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Q: Find the volume of the solid generated by revolving the region bounded by the given lines and curves…

A: y=x, y=0,x=2, x=6 We need to find the volume of solid generated by revolving the region bounded by…

Q: 15. Find the volume by the parabole y² = of the solid generated by revolving y-axis, the area…

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Q: Q4 The base of a solid is the region between the curve, y?(p + x) = x²(3p – x), 0 < x < 3p, y 2 0…

A: please see the next step for solution