Find the volume obtained by rotating the region between the curves y = 3x and y = x² about the line x = -1.

Q: Find the volume of the solid generated by revolving the region under the curve y=2x-x^2 about the…

A: Given y=2x-x2

Q: Find the volume of the solid that results when the region enclosed by the curves y = -x and x = 2y“…

A: The two functions are as follows:                    y1=14x2y2=x2 The points of intersection are the…

Q: The region enclosed by the curves y =x and y = 1 is shown below: Cross section area of the solid…

A: The solution are next step.

Q: y = 9x² and y = 0 about x = -4

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: The region bounded by the parabola y = x² and the line y = 2x in the first quadrant is re- volved…

A: Please refer the attached image for complete solution.

Q: A torus is formed by revolving the region bounded by the circle x2 + y2 = 1 about the line x = 2 .…

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Q: Find the volume of a cone generated by revolving about the y-axis the area bounded by the line…

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Q: The area bounded by the parabola x^2-2x+y=3, in the second quadrant about the line y=4. Find the…

A: Consider the given curve: y=-x2+2x+3 Here, the objective is to find the volume of solid formed by…

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

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Q: Find the volume of the solid that esults when the shaded region is evolved about the indicated axis.…

A: Solution :

Q: Set up the triple integral to find the volume inside x² + y² = 9, above z = 0, and below x + z = 4.…

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Q: find the volume about y-axis y %3D %3D X = 2tan 2. 2. 3 x

A: In the  question we have to find the volume about y axis.

Q: The region in the first quadrant that is enclosed by the x-axis, the curve y = 5/(xsqrt(5 - x)), and…

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Q: 5. Use Slicing. y = 8x, x = 0, x = 2, y = 0, re : x- axis

A: Method of Slices or Discs: To obtain the volume of solid of revolution obtained by revolving the…

Q: I FIND THE VOLUME GENERATED BY REVOLVING THE AREA BOUNDED BY THE GIVEN CURVES AND LINES REVOLVED…

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Q: explain and illustrate how you could find the volume of a sphere of radius R using the techniques of…

A: To determine: The volume of sphere of radius R using the techniques of solids of revolution. set up…

Q: The area bounded by y^2 + x - y = 1, y-axis, and the line 2y = 9 is revolved about the line x = 1…

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Q: Find the volume generated by revolving the area enclosed by the curve x^2+y^2=16 about the y-axis.

A: here volume is ∫πy2dx here the limit is if we put y=0 in equation so x range from -4 to 4 so   V=…

Q: y = 9x² and y = 0 about x = −4

A: Given:        y=9-x2 and y=0         x2=9           x=3 about x=-4

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

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Q: The area R in the plane is limited by the curves given by x = y^2 +2, y = x − 4 and y = 0, as shown…

A: Consider the given functions, x=y2+2,y=x-4 The value of y is lying between 0 to 2. the method of…

Q: The region bounded by the parabola y = x² and the line y = 2x in the first quadrant is revolved…

A: Please find the answer.

Q: The region bounded by y = 2x – x2, and y = 1 is revolved about: 1- The line x = 1 2- The y-axis Find…

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Q: Find the volume formed by revolving about the x-axis the area bounded by the curve (x + 1)^2 = 4(x -…

A: Given data:- Equation of curve, x+12=4x-1 Line, y=4

Q: (kindly answer the 2 numbers since they are connected) 1. Find the area of the region bounded by the…

A: 1st we will draw the solid formed by rotating the shaded region about y-axis .  To find volume of…

Q: Find the volume generated by revolving the area bounded by the curve y = (1 − x2)2 and the x-axis…

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Q: 4. Find the volume of the solid generated by revolving the region bounded by the graphs of the…

A: The given region is bounded the graphs of the equations y=1-x2 and y=0. The region is revolved about…

Q: Find the volume of the solid that results when the region enclosed by x = y2 and y = x is revolved…

A: Find the volume of the solid that results when the region enclosed by x =y2 and y = x is revolved…

Q: y = x4; and y = 1 about y = 2

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Q: The region bounded by the parabola y = x and the line y = 2x is revolved about the line y = -1. Find…

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Q: The region bounded by the curves y = sec x and y = 2, for 0 sxs, is revolved around the x-axis. What…

A: Given that the region is bounded by the curves y=secx and y=2 for 0≤x≤π3. Obtain the volume of…

Q: Find the volume generated by revolving the area enclosed by the curve x2 + y2 = 25 about the line y…

A: Explained below

Q: The area on the first quadrant of the circle x^2 + y^2 = 36 is revolved about the line y + 10 = 0.…

A: To find: The volume generated by the area on the first quadrant of the circle x2+y2=36 is revolved…

Q: 6. What is the volume generated when the area in the first quadrant bounded by the curve x2 = 8y,…

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Q: Find the volume generated by revolving about the y-axis the area bounded by the curve x2 = 4(x-y),…

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Q: The region in the first quadrant bounded by x2 + y² = 1, x 2, and y = 1 is revolved about: 1- The…

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Q: The area of the region enclosed by the curve y=x(x-1)(x-2) and is revolved about the x-axis. What is…

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Q: Find the exact value of the volume of the solid that results when the region bounded by y = Vĩ, y =…

A: I use shell method

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

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

Q: Please help me with this question. Thank you so much! Find the volume generated when the area…

A: We will solve the following

Q: The area bounded by the curve y = e−x, the axes, and the line x = 2 is revolved around ox. Find the…

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Q: Find the volume generated when the area bounded by the curve y2=x , the line x=4 and the x-axis is…

A: Volume bounded by the curves, about y-axis.using Disk method

Q: and the x-axis. What is the volume generated by revolving this area by the у-аxis.

A: To find the volume about y axis

Q: Find the volume if the area bounded by the curve y = x³ + 1, the x-axis and the limits of x = 0 and…

A: (As per the guidelines, only 1st question will be answered).

Q: I FIND THE VOLUME GENERATED BY REVOLVING THE AREA BOUNDED BY THE GIVEN CURVES AND LINES REVOLVED…

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Q: + 3

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Q: Find the volume formed by revolving the region about the line x = 4. 1 2 3 y = 3 – x & y = -x² + 2x…

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Q: I FIND THE VOLUME GENERATED BY REVOLVING THE AREA BOUNDED BY THE GIVEN CURVES AND LINES REVOLVED…

A: As per our guidelines we are suppose to do only one question, thus I am providing solution of first…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.