Rotation of the region in Figure 12 about the y-axis produces a solid with two types of different cross sections. Compute the volume as a sum of two integrals, one for -12 < y < 4 and one for 4 < y < 12. y= 12- 4x y = 8x - 12 -12. FIGURE 12

Q: Find the volume of the solid generated by the region bounded by y - x² = -3,x+y = 3 about y = -5.

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Q: Find the volume of the solid generated by revolving about the line y =-1 the region above the X-axis…

A: Here, for x = -1 to x = 0,  Area is bounded by  the curves 2y = x + 3  and  y2 = - x

Q: 28 The region in the first quadrant bounded by y rotate about the line x = 4x2 , 3x + y = 7, and the…

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Q: Consider the region formed by the graphs of f (x)=sqrt( x) , f (x)= 1/x and x = 2. Set up the…

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Q: Consider the region formed by the graphs of f (x)=sqrt( x) , f (x)= (1 /x)and x = 2. set up the…

A: We sketch the region using a graphing calculator. Violet curve is: f(x)=sqrt(x) Black curve is:…

Q: Consider the region formed by the graphs of f (x)=sqrt (x) , f (x)= 1/x and x=2. Which integral…

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

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Q: 15 - Which of the following is the volume of the object that occurs when the region bound by the y =…

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Q: The area bounded by y = 2x² - x³, and y=0 is revolved about x=0. Find the volume of the solid…

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Q: I need help with part b) of the problem: b) Set up an integral that represents the volume of…

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Q: Set up integral for the volume dboud y-d y=- xu X- y-2.

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Q: Consider the region between the graphs of f(x) = 5 – x and g(x) = 2x on [1,4]. For each line of…

A: Note: According to the guidelines only one question will be answered please upload other questions…

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

A: Given  y = e-3x , y=0 , x=0 , x=5 about the x-axisApply the volume formula = ∫abfx2-gx2dx

Q: 4. Consider the region bounded by y=x² and y=x in the first quadrant. What is the volume of the…

A: Disclaimer: According to the guidelines, the handwritten solutions are not provided at the moment,…

Q: Find the volume of the solid obtained by rotating the region bounded by x = -3 + y² and x = -2y…

A: Given the curve is x=-3+y2, x=-2y Outer radius=-3+y2+9=y2+6 inner radius=-2y+9 Intersection point is…

Q: The volume obtained by rotating the region bounded by y=36-(x-3)2 and the x-axis about the line x=…

A: Given Region bounded by curve  y=36-(x-3)2, x-axis  (means y=0) about line x=10. the maximum y is…

Q: 7) Suppose that y, =sinx and y, = cos x on [0,4] %3D Find the volume if the region between y, and y,…

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Q: Only one of these calculations is correct to evaluate the volume of the solid generated by revolving…

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Q: Find the volume generated by the rotation of the region defined by the curve x=y2 and the line y=x-2…

A: Given curve x=y2 and the line y=x-2. Around the line y=-1. The objective is to find the volume…

Q: Example 28 Find the volume of the solid obtained when the region bounded by the curve y= 3x, x- axis…

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Q: 3. Determine the volume of the solid obtained by rotating the region bounded by y = 2vx – 1 and y =…

A: Note: according to our guidelines we can answer only third question because student asked that…

Q: A region is bounded between x = 0, y = 1, x = 1, and y = (x-1)^2+1. What is the volume generated if…

A: *to find:- generated volume about x-axis.

Q: 5. Find the volume of the solid generated by revolving the area bounded by the curve y = 4x - x2 and…

A: We are asked to find volume of the solid

Q: 3. Find the volume of the solid formed by y = √√4sin(x) bounded by x = 0 revolved about the x axis…

A: According to the question we need to find out the volume of revolution of the curve.

Q: 2 Set up integral for the volume about y-d y=- x u X- y-2.

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Q: If the region under the graph of +++/-/1 -- y = x² + from x = 1 to x = 5 is rotated about the…

A: NOTE: Refresh your page if you can't see any equations. . the given function is  and the given…

Q: What is the volume of the solid generated when the region bounded by the graph of x = √y - 2 and the…

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Q: 2. Find the volume of the region bounded by y = x3 and y = x rotated about %3D the x-axis.

A: In this problem we can use washer method to find the volume of the solid of revolution. Washer…

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: Example 8: Find the volume of the solid whose base is bounded by y = x +1 and y = x², the cross…

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Q: Find the volume of a solid extending from y = 2 to y = 5 if every cross section has area A(y) = 5.

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Q: The line x=-3 of the region bounded by the 2x=4-y2 and 2x=y2-4 curves Calculate the volume of the…

A: We first sketch the region using a graphing calculator. 2x=4-y2 (red) 2x=y2-4 (blue) x=-3 (green)

Q: If the region under the graph of 1 x² y = x² + from x = 1 to x then the volume of the resulting…

A: The objective of the question is determine the volume and choose the correct option.

Q: Compute the volume bounded by y=x²-2x and 3y +2x²-27=0 when it is revolved around the y-axis

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Q: Use a double integral to find the volume of the indicated solid. z = 6 – x2 – y2 -1 < x < 1 -1 < ys…

A: The function is z=6-x2-y2 over -1≤x≤1 and -1≤y≤1.   Set up the integral.…

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

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Q: 2. Set up the integral(s) for finding the volume of the solid of revolution obtained by rotating…

A: We will find out the required volume of solid of revolution.

Q: 2. The area bound by the curve y = ezr, the y – axis and the line y = 4 is rotated about the line y…

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Q: The region bounded by the curve (y = x2 + 5) and the line (y = x+7) is revolved about x-axis to…

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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: 2. Consider the region bounded by y 5- x 2 , y = x- 1, and x = 1. Set up an integral to find the…

A: Region is bounded by y=5-x2y=x-1x=1 region is revolved about x axis

Q: (2,2,0)

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Q: Find the volume of the solid obtained by rotating the region bounded by x = -8+ y² and x = 2y about…

A: Given : x=-8+y2 , x=2y  and x=-9. Therefore, -8+y2=2y⇒y2-2y-8=0⇒y2-4y+2y-8=0⇒yy-4 +2y-4 = 0⇒y-4y+2 =…

Q: Find the volume x=y-y2; x=0 revolving at y-axis

A: Given problem:- Find the volume x=y-y2 ; x=0 revolving at y-axis

Q: Consider the region bounded by the graph of y2 = (4-x)^2/(1+x)^2 on the interval [0, 1]. Find the…

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Q: Find the volume of the solid generated when the region between the graphs of the equation y-1=x and…

A: Volume of the solid generated by the curves  f(x)=y=x+1 and g(x)=y=x , 0≤x≤1 is given by the formula…

Q: Sketch and set up the integrals for volume of the region bounded by y = x^2 + x - 2 and y = 3x + 13,…

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Q: 4. Find the volume of revolution generated by revolving the region between f(x) = 9-3x and f(x) =…

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Q: The base of S is the part of the region bounded between y = -4 and y = 4 - that lies in the second…

A: S is the part of region bounded between y=x24-4 and y=4-x24 that lies in the second and third…

Q: 3 4

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