4. a) Find the volume of the solid formed by rotating the region y = !, 1

Q: 2. Find the volume generated by revolving about the y-axis, the area bounded by x² + y² = a² and x+y…

A: The bounded region: Green colored    To find: The volume of revolution around y-axis of the bounded…

Q: A/ Find the volume generated by revolving the area bounded by x = y-1 and y =5 around the x-axis?

A: We will find out the volume of solid of revolution by shell method.

Q: 26. x = 4 - y, x = 16- y?

A: Given that x=4-y, x=16-y2  To find the volume about line y axis.     Formulas used: Volume of…

Q: 5. Use the cylindrical shell method to determine the volume of the solid obtained by the revolving…

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Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region…

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Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region…

A: Topic = volume

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

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Q: Find the volume of the solid formed by revolving the region bounded by the graphs of y = x2 + 1, y =…

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Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region…

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Q: (1 point) The volume of the solid obtained by rotating the region enclosed by y = a², y = 2x, about…

A: y=x2y=2x about line x=2 for point of intersection x2=2xx2-2x=0x(x-2)=0x=0,2

Q: Find the volume of revolution resulting from the region bounded by 3x-y²+2=0₂ xty = 2, and y = ³√x,…

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Q: The volume of the solid generated by revolving the region bounded by y = 2x - x² and (5a+1)π y = 0…

A: Volume

Q: 27. Find the volume generated by rotating the area bounded by y = x² + x, x = 1, x = 4, and the…

A: Given that: y=x2+x,   x=1,  x=4   and   the   x-axis To sketch the graph,

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

A: Given y=x+2 , y=0 , x=-2 , x=5about the x-axis .Volume V=π∫abfx2-gx2dx

Q: what is the volume generated if the area bounded by the cirves x2 =8y , x=4 and y= 0 is resolved…

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Q: 7. Find the volume of the solid obtained by rotating the region bounded by and r = 0 about the…

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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: 7. Use the washer method to find the volume of the solid generated by rotating the region bounded by…

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Q: 4. Determine the volume of the solid obtained by rotating the portion of the region bounded by y =…

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Q: Find the volume V of the solid S that results when the region bounded by y = x2, y = x, x = 0 and y…

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Q: 10. Use the shell method to set up (but do not evaluate) an integral representing the volume of the…

A: We will graph the functions using a graphing calculator. The shaded region is rotating about the y…

Q: 66. Find the volume obtained by rotating the region enclosed by y = In x and y = (In x)² about the…

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Q: b) Determine the volume of the solid generated by rotating the region bounded by y = V2x and y =…

A: We have given the curves

Q: Set up and evaluate the integral that gives the volume of the solid formed by revolving the region…

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Q: Let O denote the region in a circle centered at the origin of radius 1 that is bounded from above by…

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Q: Derive the formula for the volume of a sphere by revolving about the x-axis, the region bounded by…

A: We have to derive the formula for the volume of a sphere by revolving about the x-axis, he region…

Q: please set up the integral and find the volume. thankyou

A: The equation of cone with x axis as the axis of cone, is x2=y2+z2, |x|≤1 It is bounded by the planes…

Q: Sketch the region R bounded by the graphs of x = (y- 1)2 and x 9. Use cylindrical shells to compute…

A: The shell method uses a cylindrical shell of radius r, height h, and thickness dr. The volume…

Q: B. Find the volume generated by revolving the region enclosed by x - -y and y=x+2 about У-аxis. 20%

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Q: Use the Theorem of Pappus to find the volume of the solid of revolution The torus formed by…

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Q: Area bounded by y2 x = -1 = x and x – y – 2 = 0, revolve about

A: Let the element at distance y from the x-axis,  The distance of the curve y2=x from the axis x = -1…

Q: 1. Find the volume of the solid obtained by rotating the region bounded by the curve y? = x?(a – x),…

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Q: Find the volume of the solid generated by revolving about the y-axis, the area bounded by y = x^2 ,…

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Q: Use the Shell Method to compute the volume of the solids obtained by rotating the region enclosed by…

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Q: 8. Set up and evaluate the integral to find the volume of the smaller region cut from the solid…

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Q: Find the volume obtained by rotating the bounded region given by y = 0 and y = x (1 – x) around the…

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Q: Use the Theorem of Pappus to find the volume of the solid of revolution obtained by rotating the…

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Q: Calculate the volume of solid Q limited by surface z

A: Consider the solid Q: Clearly, 0≤z≤11+x2+y2Let x= r cos θ       y=r sin θ⇒x2+y2=r2Projection on the…

Q: Find the volume generated by revolving the area 1 bounded by y -, x = 3, x = 9, and y O about the…

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Q: Use the method of disks/rings to determine the volume of the solid obtained by rotating the region…

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Q: 3. Find the volume generated by revolving the area bounded by the parabola y² = 8x and its latus…

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: = 3, Find the volume of the solid obtained by rotating the region bounded by y = x , y = 0, and a =…

A: In this question we have to just find the volume generated by rotation.

Q: Consider the region bounded by y = tan r, r-axis, and a = whose graph is shown below. 0.5 0.5 -0.5…

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Q: (5) Find the volume and draw an illusration of the solid S obtained by rotating the region bounded…

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Q: 6. Find the volume of the solid obtained by rotating the region bounded by the given curves about…

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Q: Find the volume of the solid whose base is the region bonded by y=x^2 and y= 1-x^2 and whose cross…

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Q: 3. Use Use the disk method to determine the volume of the solid obtained by the revolving the region…

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Q: 9. Find the volume generated by revolving the given plane area about the given line using the disc…

A: We are given two regions: (a) y=2x2, y=0, x=0, x=5 about x-axis. (b) x2-y2=16, y=0, x=8 about…

Q: 23. What is the volume of the solid bounded below by the plane z=y and above the circular region D…

A: We have to choose the correct answer from the given options according to the given information

Q: Find the volume of the solid that results when the region bounded by y = x and y = x², from x = 0 to…

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