30 Find the volume of the solid generated by rotating the region bounded by the curve y=(x-2) and the line y=x through 360° about a. the x-axis b. the y-axis

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

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Q: Find the volume of the solid generated by re-volving the region in the first quadrant bounded by the…

A: We need to find the volume of the solid generated by revolving the region in the first quadrant…

Q: Find the volume of the solid of revolution formed by rotating the region bounded by the parabola…

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Q: b) 1: Find the volume of the solid obtained by rotating the region bounded by the curve about the…

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Q: (c) Find the volume of the solid generated by revolving the region in the first quadrant bounded…

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Q: Find the volume.

A: Find the region R in the x-y plane.The x-axis is y = 0 and y axis is x = 0 line.R is the region…

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

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Q: Q.4. Find the volume of the solid that results when the region enclosed by the curve y3sinx, y = x…

A: Volume problem....

Q: 4. (a) Find the volume of the solid generated when the region enclosed by y = -. 6-x2 and y = 0 is…

A: Given the solid generated when the region enclosed by  y=−6−x225  and  y=0   is revolved around the…

Q: Q1/ Find the volume of the solid generated by revolving the region bounded by the line (y= x+3 ),…

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Q: ind the volume V of the solid obtained by rotating the region bounded by the given curves about the…

A: Given query is to find the volume generated when revolve the curves around y = 5.

Q: Find the volume (in units3) of the solid generated by revolving the region under the curve y = 4e−2x…

A: I use cylindrical shell method to find volume about y axis

Q: Q.5 Find the volume of the solid whose base is the region enclosed between the curve x=1-y and the…

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Q: 4. Find the volume of the solid generated by revolving the region enclosed by the graphs of y = e* ,…

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Q: (a) sketch the region enclosed by the curves, (b) describe the cross section perpendicularto the…

A: a) We sketch the region using a graphing calculator Red is y=16-x Blue is y=3x+12 Green is x=-1 The…

Q: Find the volume of the solid obtained by rotating the region between the curves y = 3x - x³ and…

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Q: 2. Sketch the graph and shade the region enclosed by the curves y = x² and x axis from x=0 x=2. Find…

A: Given region enclosed by - y = x2 x =0 x =2

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

A: For rotation about Y axis, the graph will be as shown,

Q: 30 Find the volume of the solid generated by rotating the region bounded by the curve y= (x- 2)° and…

A: We first find the intersection of these two curve

Q: Consider the region R bounded by the line y = 42- 8x and the parabola y = 27 - x2. To find the…

A: We need to find volume.

Q: (d) Find the volume of the solid generated by revolving the region in the first quadrant bounded…

A: Solution:Giveny=2 and y= sec x tan xTo find the volume of solidFormula:Volume=π∫ab(y1-y1)2dx∫k…

Q: 1. Find the volume of the solid that results when the shaded region is revolved about the X - AXIS.…

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Q: Find the volume of the solid generated by re-volving the region in the first quadrant bounded by the…

A: First calculate the area ‘A’ under the given curve as.

Q: ind the exact volume of the solid generated by revolving the region bounded by the given curves…

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Q: 6. Consider the region created by revolving y = 4 +x, y = 3 – x, x = 0, and x = 2 about the y -axis.…

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Q: Find the volume of the solid of revolution generated by revolving the region in the first quadrant…

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Q: 5. Use the shell method to find the volume of the solid obtained by rotating the shaded region about…

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Q: Rotate the region specified above by the curve y = x and beneath by the curve y = x2 from x = 5 to x…

A: Explained below

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

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Q: 4. Find the volume of the solid formed by rotating the region under the graph of f(x) = 1 on [0, 3]…

A: Volume of a solid generated by rotating the graph of a function can be determined using the method…

Q: 1. Find the volume of a solid if the area boun ded by the curve y = In x, the x-axis and the line x…

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Q: b) Find the volume of the solid obtained when the region under the curve y= 2-x , x=0,y%3D0 revolved…

A: We will find out the required volume of solid of revolution using cylindrical shell method.

Q: c) the volume of the solid found by rotating the region bounded by the given curves about the…

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Q: 19. Find the volume of the solid that results when the region enclosed by = 2y, y = 2, y = 3 and x =…

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Q: Find the volume of the solid that results when the region enclosed by the given curves y = e-2, y =…

A: The given curves are; y=e-2x, y=0, x=0 and x=1 So, the bounded region is as shown below. Apply the…

Q: (b) Find the volume of the resulting solid if the region under the curve 1 from x = 0 to x = 1 is…

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Q: 3- a) Find the area of the region in the first quadrant between, y = x and y = x² b) Find the volume…

A: (a) The given region is y=13x12 and y=23x2. We have to find the area of the given region.

Q: 5. Use Shells to find the volume of the solid generated by revolving the region in the first…

A: FORMULA FOR CYLINDERICAL SHELL METHOD V=2π∫ab(x-h)f(x)dx According to question, The volume is in…

Q: Consider the region enclosed by the curves y=2+1 and y= 2z+1: The volume of the solid generated by…

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Q: 9. Find the volume of the solid obtained by rotating about the x-axis the region enclosed by the…

A: We sketch the situation first The shaded region is rotating about the x-axis.

Q: The volume of the solid generated by revolving the curve y = 2 x, between x =0 and x=3 about the x-…

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Q: 2. Consider the region bounded by the y-axis, y = 3x+ 1, and r 4. Find the volume of the solid…

A: Given function are y=3x+1x=4y axisAxis of rotation y=-5

Q: Find a curve such that when the portion of the curve from x = a to x = b is rotated around the…

A: Let the curve be y=fx.  The curve is rotated around X-axis from x=a to x=b.  The surface area of…

Q: Use the cylindrical shell method to calculate the exact volume of the solid formed by rotating the…

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Q: The volume of the solid generated by revolving the region bounded by the curve y = cos x, 0Sxs about…

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Q: Rotate the region specified above by the curve y = x and beneath by the curve y = x^2 from x = 0 to…

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Q: Find the exact volume V of the solid obtained by rotating the region enclosed by the graphs of y = e…

A: The given region enclosed by the graphs: y=e-x, y=1-e-x The graph of the above region:           To…

Q: 12. Find the volume of the solid generated by revolving the region bounded by the curve y = sin x…

A: F(x) = sinx-2

Q: 1. Find the volume of the solid formed by revolving the region bounded by the graph of y = 3x + sin°…

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Q: Q2: Find the volume of the solid generated by revolving the region between the curve y = x and the…

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.