Find the volume generated by revolving about the line x - 4 = 0 the area bounded by the curve x2 = 8y and the line v – 2 = 0.

Q: . Find the center of mass of a thin plate covering the region bounded below by the parabola y = x…

A: The given curve is, y=x2 and the line y=x with density δx=12x. Sketch the bounded region as below:

Q: Find the volume of the solid obtained by revolving the curve x²=y-3 about x-axis from x=1 to x=3

A: The volume generated by revolving any curve y=f(x) about x-axis  from x=x1 to x=x2 is given by V=…

Q: Find the volume of solid generated by revolving the area bounded by y³=x, y=2 and x=0 about the…

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Q: Find the volume of the solid generated by revolving the region bounded by y = 4x - x and y = 0 about…

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Q: Find the volume of the solid formed by revolving the area bounded by the parabola y2 = 9x and the…

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Q: Find the volume of the solid generated by revolving the region between the parabola x = y² +1 and…

A: Given Data: Curve 1: x=y2+1 ......(1) Curve 2: x=5 ......(2) The graph of the region enclosed by the…

Q: the area between the curves 4y=x2 and y2=4x is revolve about the line x= "-1." solve for the volume…

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Q: Find the moments and center of mass for the thin plate covering the region between the x-axis and…

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

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Q: Find the volume of the solid generated by revolving the regionbounded by y = √x and the lines y = 2…

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Q: Find the volume of the solid generated byrevolving the region in the first quadrant bounded by the…

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Q: Find the volume of the solid generated by revolving the region between the curve y = 10 – x² and the…

A: The region is bounded by y=10-x2 and y=1. By Cylindrical shell method, ∫ab2πyfydy Obtain the…

Q: Find the volume of the solid generated by revolving the regionbounded by the parabola y = x2 and the…

A: To find volume of solid

Q: FIND THE VOLUME OF THE SOLID GENERATED WHEN THE REGION BOUNDED BY THE CURVE (x-5)² = 4-Y AND THE…

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Q: Find the volume of the solid generated when the area bounded by the curve y = Vx, the y-axis, and…

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Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

A: • This is a problem based on the applications of definite integral.  First we have to identify the…

Q: Find the volume of the solid generated by revolving the area bounded by x- y2 + 6y-9 0 and x- y-9 =…

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Q: Find the volume generated by revolving about the line y – 1 = 0 the area bounded by the curve x2 =…

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Q: Find the volume generated by revolving the area enclosed by the curve x^2 + y^2 = 25 about the line…

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

Q: Find the volume of the solid generated by revolving the area bounded by x - y² + 6y - 9 = 0 and x -…

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Q: Find the volume of solid generated by revolving the region bounded by the curve y-4/x' and the lines…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Find the volume of the solid generated by revolving the region bounded by the line y = 0 and curve y…

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Q: Find the volume of the solid generated by revolving the area bounded by x2 – 2kx – 3ky + k² = 0 and…

A: Given curves are:  x2-2kx-3ky+k2=0 3x-3y+k=0 The area bounded by them is revolving about the line…

Q: Find the volume of the solid generated by revolving the region between the parabola x=y^2+1 and the…

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Q: ut the line x = 3.

A: The parabola equation is given , x2 = 4y. The equation of line is given , x = 4 - 2y. The volume…

Q: Find the volume of the solid generated by revolving the region bounded by the curve y = sin x and…

A: Given:Find the volume of the solid generated by revolving the region bounded by the curve y = sin x…

Q: Find the volume of the solid generated by revolving the region bounded by y=r+3, リ= and エ=5 about…

A: Identify the limits of integration from the region. Since the region is bounded by the lines y=x+3,…

Q: Find the volume of the solid of revolution generated by rotating about x= -1, the region bounded by…

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Q: Find the volume of the solid obtained by revolving the region in the first quadrant bounded by…

A: We need some modification I'm original formula to solve this problem. Let's see what modification we…

Q: Find the volume generated by revolving the area enclosed by the curve x2 + y2 = 16 about the y-axis

A: Given Data: Curve: x2+y2=16   The figure below indicates the graph of the curve.   The intersection…

Q: Find the volume generated by the region bounded by the curve y 12X and the line X3 rotated about the…

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Q: Find the volume of the solid generated by revolving the specified region about the given line. R…

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

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Q: Find the volume of the solid generated byrevolving the region in the first quadrant bounded by the…

A: Using Shell Method:             2π∫01x.e-x dx Limits come from where the column can be created. (in…

Q: Find the volume of the solid generated by revolving the region bounded by y = x² – 2x + 2 and y = x…

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Q: Find the volume of the solid generated by revolving the area bounded by x² – 2kx – 3ky + k² = 0 and…

A: Given curves are:  x2-2kx-3ky+k2=0 3x-3y+k=0 The area bounded by them is revolving about the line…

Q: Find the center of the mass of a thin plate of constant density 6 covering the region bounded by the…

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Q: Find the volume of the solid generated when the region under the curve y = x² over the interval [0,…

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Q: Find the volume of the solid generated by revolving the regionbounded by the parabola y = x2 and the…

A: Given parabola y=x2 and the line y=1 about the line y=2limits of integration are x=-1 to x=1radii of…

Q: Find the center of mass of a thin plate covering the region bounded below by the parabola y = x 2…

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

A: From the formula of the region  rotating about a line parallel to y axis.( Disc method) after doing…

Q: Find the center of the mass of a thin plate of constant density ô covering the region 3 bounded by…

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

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

Q: Find the volume of the solid obtained when the region enclosed by the curve x=2-y² and find the x=y…

A: Draw the sketch of the given curve and lines.

Q: Find the volume generated by revolving about the line x – 4 = 0 the area bounded by the curve x^2 =…

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Q: Find the volume of the solid generated by revolving the unbounded region lying between y = −ln x and…

A: Given that: y=-lnx   and   the   y-axis To sketch the region:

Q: Find the volume of the solid S obtained by revolving the region bounded by the curves y = Vx +1 and…

A: Rewrite the given equations, to identify the functions f(y) and g(y). Also, find the point of…

Q: Find the volume generated by revolving the area bounded by the parabolic arc Vx + Jy = Va and the…

A: Given problem:- Find the volume generated by revolving the area bounded by the parabolic arc √x + √y…