4. Find the volume of the solid generated by revolving about the y-axis the region in x = 4y – y? and x = 4 - y

Q: (1) Find the volume of the solid obtained by revolving about the y-axis the region bounded by y =…

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Q: The graph of the volume for solid revolution between the curves y = x+1 and y = O around the x -…

A: Plot the lines and determine the area bounded by these lines. Use the area and the rotation about…

Q: 2. Determine the volume of the solid obtained by rotating the region bounded by y = 4x and y = x³…

A: The volume of revolution of the area bounded by the curves y1=f1(x) and y2=f2(x)  between the limits…

Q: 2. Find the volume of the solid formed by revolving the region bounded by the graphs of x = -y² +…

A: Here we have given a solid region bounded byx=-y2+4y,y=1and x=0. So bounded solid region will be…

Q: 8 Use the method of cylinders to determine the volume of the solid obtained by rotating the region…

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Q: 12. Find the volume of the solid that results when the region bound by x 1-y and the y-axis is…

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Q: 3. Find the volume of the solid generated by revolving the area bounded by the curve y = x' and the…

A: Topic:- application of integration

Q: 6. Find the volume of the solid formed by rotating the region enclosed by y=e2x+5, y=0, x=0, x=0.6…

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Q: 5. Find the volume of the solid generated by revolving the region bounded by y = e-x², the x-axis,…

A: The given equation is y=e-x2. Find the volume of the solid rotated about the y-axis.

Q: 14. Find the volume of the solid region generated by revolving the region bounded by y = 1-x² and y…

A: Here given, y=1-x2 and y=0, Then 1-x2=0⇒x2=1⇒x=±1

Q: 3) Determine the volume of the solid obtained by revolving the region bounded by 2x + y – 6 = 0, x-…

A: Volume of revolution

Q: Consider the region bounded by the graph of y2 = (6 – x)2 (1 + x)2 on the interval [o, 1]. Find the…

A: Given: y2=6-x21+x2 To Find: The volume of the solid generated by revolving the region about the…

Q: A region bounded byf (y) = Vỹ + 1, y = 4, y = 9, and x = 1 is shown. What is the volume of the solid…

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Q: 1) Calculate the volume of the solid created by rotating the region bounded by y = x² +1 y = -x + 3…

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Q: Only one of these calculations is correct to evaluate the volume of the solid generated by revolving…

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Q: 4. Find the volume of the solid obtained by rotating the region bounded by the given curves about…

A: Given that y=ln x, y=1, y=2, x=0 find the volume about y-axis V=π∫12x2 dy

Q: 3-Find the volume of the solid obtained by rotating the region bounded by y=2x+1, x=4 and y=3 about…

A: .

Q: 1. Determine the volume of the solid obtained by rotating the region bounded by the curves y = x? -…

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Q: 2(/ỹ),x = 0, y = 9 Find the volume of the solid generated by revolving the region bounded by x =…

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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: 16. Find the volume of the solid generated by revolving the region bounded by the curve y = x – x²…

A: To find the volume of the solid generated by revolving the region bounded by the curve y=x-x2 and…

Q: 2) ( ) Sketch and find the exact volume of the solid obtained by rotating the region B bounded by…

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Q: 2. Find the volume of the solid generated when the region between y = sin x and y = 0 for 0 ≤ x ≤ π…

A: The region between y=sin x and y=0 for 0≤x≤π is revolved about the y-axis.

Q: 4) Find the volume of the solid generated by revolving the region around the y-axis y = Vx – 1 x…

A: Let us use disc method to find the volume. After revolving about the y-axis, the solid generated is…

Q: 3. Find the volume of the solid generated by revolving about the line x = 3 the region in y = 2x2 –…

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Q: 3) Find the volume of the solid generated by revolving the region bounded by y = cos x, y = sin x, x…

A: According to the company policy, we will answer only the first question. Please resubmit the second…

Q: 4) Find the volume of a solid generated by revolving about the x- axis the region bounded by y = x2…

A: We find the volume of a solid generated by revolving about the x- axis the region bounded by y = x2…

Q: 1. Find the volume of the solid of revolution generated by revolving the region bounded by y = x?…

A: Given problem:-  Find the volume of the solid of revolution generated by revolving the region…

Q: Only one of these calculations is correct to evaluate the volume of the solid generated by revolving…

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Q: Find the volume of the solid generated by revolving about the y-axis the region bounded by the given…

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Q: 21/ Find the volume of the solid generated by revolving the regic bounded by y = \cos x , y = 0 &…

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Q: 2. Sketch the solid generated when the region between the graphs of the equations y = +² and y = x…

A: The objective is to sketch the solid generated when the region between the graphs of the equations…

Q: 5. Find the volume of generated by rotating the region bounded by x = 4y – y? and x = 0 (a) about…

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Q: 1. Use your preferred method to calculate the volume of the solid obtained by revolving the region…

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Q: 4. Find the volume of the solid generated by revolving the region bounded by y = x 2 + 2 and y = x +…

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Q: 4. Find the volume of the solid generated by revolving the region bounded by the curves y = 2-x² and…

A: Given problem:- Find the volume of the solid generated by revolving the region bounded by the curves…

Q: 6. Find the volume of the solid formed by revolving the region bounded by the graphs of y = x2, x =…

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Q: 6. Find the volume of solid generated by revolving bout the y² = 4x, x = 0, y = 4 about y = 4.

A: Given curves are, which generate the solid y2=4x, x=0, y=4   Graph is Since y2=4x⇒y=4x

Q: 5. Find the volume of the solid obtained by rotating the region bounded by y = x³,y = 0, x = 1 about…

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Q: Calculate the volume of the infinite solid obtained by rotating the region under y = (x2 + 1) −2 for…

A: Use shell method and find the volume.

Q: 3) Find the volume of the solid that is generated by revolving the region bounded by y= sin z cosz…

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Q: 4.Find the volume of solid generated by revolving the regions bounded by the curve y = |cos(÷)y, -2…

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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: 4. Find the volume of the solid obtained by rotating the region bounded by y = e", y = 0, x = -1, x…

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Q: 9. Find the volume of the solid generated by revolving the region bounded by the lines and curves y…

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Q: 5. Find the volume of the solid obtained by rotating the region bounded by y = x³,y = 0, x = 1 about…

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Q: 6) Use the washer method to find the volume of the solid generated by revolving the region y = x² +1…

A: We first sketch the region using a graphing calculator. From the graph, we see that x is from 0 to…