15. a) Sketch the region enclosed by the linex = 3 and y = 1 and the curve xy = 9, %3D and find its area. b) Find the volume of the solid obtained by revolving the region in Question 15 around the x-axis, using any valid method.

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

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Q: 5. Find the volume of the solid generated by revolving the area of a circle: (x - 2)² + y² = 4;…

A: In this question, we need to find the volume of solid generated by revolving the area of the given…

Q: 1. Find the volume of the solid generated when the region bounded by y = 9- x² and y = 2x +6 is…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 2. (a) Based on the diagram 1, find the intersection points between curves y=r' and Hence, find the…

A: The point of intersection of two curves is the place where the two curves meet.y=f(x) To find the…

Q: b) Find the volume of the solid obtained by rotating the region bounded by the curve y = -x² + 11…

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Q: 3. Find the volume of the solid generated when the region enclosed by y = v2x + 8, y = x, x = 0 is…

A: Given

Q: 3 14. Find the volume of the solid that results when the region bound by y = x°, x = 2 and the…

A: The given region is the region bounded by y=x3,x-axis y=0 and x=2. To find the volume when the…

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

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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. Obtain the volume of the solid that occur when the small side of the circle x +y =2 and the…

A: Graph of the given curves looks like this,

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

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Q: 5. Use the method of Washers and Shells to find the volume of the solid generated when the region R…

A: Given:

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: 1- Find the volume of the solid generated be revolving the shaded region about the given axis. About…

A: The volume of the solid generated when the first given region is revolved around the y-axis is to be…

Q: 4. Find the volume created by the rotation round the x-axis of the part of the curve y² = 3x %3D…

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

A: Note: As per our guidelines we are instructed to solve only one problem. Hope you understand.    The…

Q: 4- Find the volume of the solid generated by revolving the region about y-axis,the region in the…

A: Draw the graphs of y=x2, x=2 and identify the region bounded by the curves. The required region is…

Q: 2.4. Find the volume of the solid generated by revolving the region bounded by y = 5a about the…

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Q: (b) Find the volume of the solid generated by revolving the region between the parabola, y? = x – 3…

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Q: a. The volume of the solid generated by revolving the region bounded by y= 4yx and the lines y =…

A: Given that, y=4x,y=414 and x=0. Obtain the limit of the region. 4x=414 x=14 x=14 Sketch the region…

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

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Q: 13. The region bounded by y = x°, y = 0, and x = 2 is revolved about the line x= 2. Find the volume…

A: Formula: The volume of the solid revolution generated by using disk method is given by,…

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

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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: y = x² +9 %3D y= 18

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Q: 2) Use the Disk/Washer method to find the volume of the solid created by rotating the region bounded…

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Q: 2. Use cylindrical shells to find the volume of the solid generated when the shaded region is…

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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: 4. Find the volume of the solid that lies within both the cylinder a²+y² = 1 and the sphere a2+y² +…

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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: Consider the region enclosed by the curves y = x²+1 and y = 2x + 1: 5- The volume of the solid…

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Q: What is the volume of the solid whose base is the interior of the parabola y2 = x from x=0 to x=4…

A: Volume of the solid obtained by revolving y=f(x) between x=x1 and x=x2 about x-axis  is,…

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: 4. Use cylindrical shells to find the volume of the solid generated when the region enclosed between…

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

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Q: (b) Use Disc method to find the volume of the solid formed by revolving the region bounded by f(x) =…

A: Integrals and derivatives are considered as inverses of each other. For example if we have a…

Q: Find the volume of the solid generated by revolving the region between the parabola x = y? + 1 and…

A: this problem is solved using shell method..

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: Consider the region enclosed by graphs of y = x^2, x = 0, and y = 9. Find the exact volume of the…

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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: What is the volume, in cubic units, of the solid obtained by rotating the region bounded by y = 4x-…

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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: A- Find the volume of the solid generated by revolving region Under the curve (y=4-x²), about x = 2

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

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

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