4. Find the exact volume of the solid obtained by rotating the region bounded by y= 3+2x-x² and y =3-x about the y-axis. (see graph below) You may use any of the three methods we studied. Also, sketch a typical disk, washer, or shell – depending on the method you choose.

Q: 3. Find the exact value of surface area of the solid that is described by the intersection of the…

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Q: The region bounded by the graphs of y=x^2 and y=6-|x| is revolves around the y-axis. What is the…

A: solution is given below

Q: 5. Find the volume of the solid obtained by rotating about the x - axis of the region bounded by y =…

A: We have to compute the volume of the solid generated by revolving the region bounded by the curve…

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. (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: 2. Suppose that the triangle with vertices (-1,-1), (0, 1) and (1,–1) is revolved about the y –…

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Q: 8. Find the volume of the solid obtained by rotating the region R enclosed by y = x² and y = 2 - x²…

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Q: Find the volume of the solid that results when the region enclosed by x = - y² + 7, and x = y + 4 is…

A: We first find the y values of the intersecting points by setting the equations…

Q: 11. Find the volume of the a 3-dimensional solid whose base is given below and whose cross sections…

A: TO FIND THE VOLUME OF SOLID GIVEN BELOW FORMED BY THE CURVES  y=4-x2 ; y=0 ;x=0 by using the concept…

Q: Now we can say that the volume of the solid created by rotating the region under y = 8e-X and above…

A: We will find out all the unknown values.

Q: 4. Find the volume of the solid obtained by rotating about the y-axis the region bounded by y = 2x2…

A:

Q: Find the volume of the solid generated if the region bounded by the parabola y^2 = 4px (p>0) and the…

A: Given that equation of parabola y2=4px, p>0  equation of line x=p We have to find volume of the…

Q: If the region under the graph of y = 3x +4 from a axis, then the volume of the resulting solid is 2…

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Q: 10. Find the volume of the solid whose base is bounded by the graphs of the equations given below…

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Q: 3. If the region bounded by the curves y =x, y=0, and x =9 is the base of a solid, and cross…

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Q: What is the exact volume of a solid that is formed by rotating the region bounded by g (x) = †x² +1,…

A:

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

A: Given y2=4ax and y=x Volume rotating about y- axis = π ∫ab x22 - x12 dy

Q: 3. Find the volume of the solid whose base is the region in the first quadrant between the curve y=…

A:

Q: 2. Find the volume of the solid that results when the shaded region is revolved around the Y - AXIS.…

A: Volume by revolving a curve.

Q: Find the volume of the solid generated when the region bounded by the graphs of the equations x= y -…

A:

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: What is the exact volume of a solid that is formed by rotating the region bounded by g (x) = †x²+1,…

A:

Q: Below are two perspectives of the solid bounded by surfaces: y2 = x2 + z2 and x2 + y2 + z2 = 16, in…

A: In given question, concept of Triple Integrals in Spherical co-ordinates is applied. Triple…

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: 6. Find the volume of a solid whose base is the region bounded by y = 4 – x² and the x-axis and…

A:

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

A: We have given; The diagram of the given curve will be;

Q: The region bounded by y = 3x - 9 andy = -3x2 + 18 x - 9 revolved about the y-axis. Find the volume…

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Q: y = x² +9 %3D y= 18

A:

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: and y=2 8) x = y² +1₁ x = 0, you, The most appropriate method to use to find the volume generated by…

A: The given region is x=y2+1,x=0,y=-1 and y=2. Find the volume generated by revolving the region about…

Q: Q6 If the region bounded by 1 y X = 1 and x = 2 %3D is revolved about the y-axis , then the volume…

A:

Q: 3. Find the volume of the solid generated by revolving about the line x = -4 the region bounded by…

A: Solution...

Q: (2) Find the volume of the solid obtained by rotating the region bounded by the given curves about…

A: Note: Hi! Thank you for your question. As per the guideline we can solve one question at a time in…

Q: consider the region bounded by y = 2-x, y=x, and x=0. the volume of the solid if the region is…

A:

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: 8. Find the volume of the solid that results when the area of the region enclosed by y = 2x2, x = 2,…

A:

Q: A solid of revolution is generated by rotating the region between the x-axis and the graphs of…

A:

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

A:

Q: 13. Find the volume of the solid generated by revolving the area of a circle: (x − 2)² + y² = 4;…

A: The volume of the revolution of the function y=fx from x=a to x=b about the x-axis is: V=∫abπy2dx…

Q: The solid formed when the region bounded by y=x, y=2x+ 2, x=2, and x=6 is revolved about the y-axis.…

A: Given the solid formed when the region bounded by y=x, y=2x+ 2, x=2, and x=6 is revolved about the…

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

A:

Q: The base of a solid is bounded by the graph of x² + y² = a², where a > 0. Find the volume of the…

A: The base of the solid is the disk x2+y2≤a2, where a is the radius as shown below: The boundary…

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

A:

Q: 4 8. What is the volume of the solid generated when the region bounded by y= V4 +3x – x and y = 2 is…

A:

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

A:

Q: 2. Find the volume of the solid that results when the shaded region is revolved about the indicated…

A:

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…

Q: 5. Find the volume of the solid generated by revolving about the x-axis the smaller area bounded by…

A: Solution :- As per guidelines . I do first only.