5. Find the volume of the solid obtained by rotating about the x - axis of the region bounded by y = x, x = 8 and the x - axis.

Q: b- Find the volume of the solid formed by revolving the region bounded by: y=x² –1 from x =-1 to x=1…

A:

Q: Consider the region bounded by the graphs of y = x √16 - x2, y = 0, x = 0, and x = 4. Find the…

A: According to the shell method, the volume of a solid generated by revolving the region about the…

Q: 2. Solve for the volume of solid of revolution formed by rotating the area bounded by y = x² + 2, x…

A:

Q: Calculate the volume V of the solid obtained by rotating the region under y = x2 about the x-axis…

A: To find the volume V of the solid obtained by rotating under a region, use the formula, V=∫abπ(y)2dx…

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

A:

Q: 16. Find the volume of the solid generated by revolving the region enclosed by y = 3sinx and y = 0…

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Q: Find the volume of the solid formed when the region bound by y = e* + 3, x = 0, x = 3 and the x-axis…

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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 =…

A:

Q: 1. Find the volume of the solid obtained by rotating the region of the plane bounded by the curves y…

A:

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: 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: 4.Find the volume of the solid that is obtained by rotating the region bounded by y = /x +1, y = Vx…

A:

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

A:

Q: (#4) Find the volume of the solid bounded by y = 2x, y = 0, and x = 4 rotating on the x-axis:

A: Given a solid is bounded by the curves y=2x , y=0 and x=4 rotating on the x- axis.

Q: 4- Find the volume of the solid obtained by rotating about the x-axis the region under the curve y =…

A: Given curve, y=5x from 0 to 4.

Q: 1)Find the volume of the solid generated by revolving the plane region bounded by the graphs of y =…

A:

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

A: Proceed as shown below

Q: 4. Determine the volume of the solid obtained by rotating the region bounded by y = x² - 4x + 5, x…

A: as per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: 1. Find the volume of the solid generated when the region bounded by y = 9 - x? and y = 2x + 6 is…

A:

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. 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: 30. Find the volume obtained by rotating the region bound by the graph y = e"+e-2#, x = -2, = 3 and…

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

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: 2. Find the volume of the solid generated by revolving the shaded region about the given ах x+ 2y -…

A: I use cylindrical shell method for both Questions

Q: 3) Find the volume of the of the solid that results when the region endosed by the curves y = Vx, y…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: (4) Find the volume of the solid obtained by rotating the region bounded by y y=√x about the y = 1.…

A:

Q: 1- Find the volume of the solid obtained by rotating the region bounded by the curve y = 4 - r and…

A: The volume of the solid of the revolution of the curve y=f(x) obtained is  Volume=∫abA(x)dx  or…

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: Find the exact volume of the solid whose region is bounded by y = 2 a + 2, y = 0, x = 3 and x =…

A: Given data : y=2x+2 , y=0x=3 , x=4

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 obtained by rotating the region bounded by the given curves about…

A:

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

A:

Q: 1. Find the volume of the solid obtained by rotating the region of the plane bounded by the curves…

A: Given: The curve are y = x, and  y = x4 To find: The volume of the solid

Q: 23. Find the volume of the solid formed by the region in the first quadrant bounded by: x = y - y, x…

A: *to find:- Volume of revolution of solid.

Q: 4) (6.) Find the volume of the solid formed from the region between y = e*, y = 0, x = 0, x = 1…

A:

Q: 2. Find the volume of the solid generated by revolving the area bounded by the given curve x + y =…

A: Given: x+y=6, y=3, x=0 for finding the volume, first we draw region bounded by given curve as below

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 resulting solid of revolution located in the first quadrant bounded by the…

A:

Q: 2) () Find the exact volume of the solid obtained by rotating the region B enclosed by the curves…

A: Volume of solid of revolution by the area enclosed by y=f(x) and y=g(x)about x-axis  (where…

Q: 2. Find the volume of the solid generated by rotating the region bounded by y =÷x³ and %3D y = 6x -…

A:

Q: 2. Find the volume for the solid generated by taking the area enclosed by f(x)=cos(x), x=0, x = and…

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Q: 6. Find the volume of the solid obtained when the region bounded by y ==, y = 0,x = 1, and x = 2 is…

A: As per the our guideline, we are supposed to solve only first question. Kindly repost other question…

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

A:

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

A:

Q: 15. Find the volume of the solid obtained by rotating the region bounded by xy = 4 and y = (x – 3)…

A: Given :  xy=4  and  y=x-32. Therefore, x-32=4x⇒xx2-6x+9=4⇒x3-6x2+9x-4=0⇒x-12x-4=0Therefore, x=1 ,…

Q: 1. Sketch the region enclosed by the curves of y = x² – 2x. y=x+4, x =-2, x = 5 and find the area of…

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Q: Find the volume of the solid obtained by revolving the region between the graph of y2 − x2 = 1 and…

A: We first sketch the region using a graphing calculator.  The shaded region will rotate about y=2…