Example 28 Find the volume of the solid obtained when the region bounded by the curve y= 3x, x- axis and the line x=1 is revolved about the x-axis through 360°. y = 3x2

Q: 8. Suppose you revolve the region completely about the of revolution. Describe the solid and find…

A: Introduction: A stable of revolution is a stable determine created via way of means of rotating a…

Q: Example 5 Find the area of the region enclosed by x = y² and y = x – 2, integrating with respect to…

A: We have to solve given problem:

Q: 4. A metal plate, with constant density 2 gm/cm² is bounded by the curve y = x², the x – axis, and x…

A: Given: A metal plate, with constant density 2 gm/cm2  is bounded by the curve  y = x2  and x = 1…

Q: Upon the release of the new Pac-Man movie, Pac-Man: Integral Adventure II, Midway has decided to…

A: Solid generated by rotating a bounded region, we use the circular disc method to evaluation of…

Q: Example 2 Determine the volume of the solid obtained by rotating the region bounded by y= Vx, x 8…

A: Region bounded by the y=x3, x=8 and x-axis

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

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Q: 3. Find the volume of the solid of revolution formed by revolving the region bounded by the graphs…

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Q: 1. vetermine the volume of the solid obtained by rotating the region bounded by the curves y = x2 –…

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Q: The volume of the solid of revolution obtained by revolving the region enclosed by the x-axis and…

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Q: 4. The region bounded by the curve y = x² + 1 and the line y = -x + 3 is revolved about the x-axis…

A: We have to find the volume of solid.

Q: 1. Sketch the graphs of v = 2x - x2 and y = - x. Shade the region bounded by the curves, Find the…

A: Given, The sketch graph of; Y = 2x - x² Y = - x The volume of the solid that is formed by revolving…

Q: A lamina is in the shape of the region bounded by the lines x = 1 and y = 2, and the parabola y =…

A: Let's find.

Q: Suppose you revolve the region completely about the line y-3 to sweep out a solic of revolution.…

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Q: a) Find the intersection point between curves 2=-2 and y=-/2x+2. Hence, find the area of the…

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Q: The diagram in Figure 3 shows the shaded region enclosed by the lines x = -1, x = 2 and the curves y…

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Q: 4. A solid is obtained by rotating about the x- axis. The curve is given to be as y = 3x² – x3 -…

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Q: x=y2 x=2-y2 What is the volume of the shape formed by rotating the region bounded by its curves…

A: Integration of function expression with respect to variable x or y gives the area between function…

Q: 9. Sketch the solid obtained by rotating the region underneath the graph of the function f(x) = Vx2…

A: The answer is in step 2.

Q: EXAMPLE 2 Find the volume of the solid obtained by rotating about the x-axis the region under the…

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Q: Example 2 Determine the volume of the solid obtained by rotating the portion of the region bounded…

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Q: Example 2.4.2. Find the volume of the solid of revolution of the region enclosed by the parabola y =…

A: Topic = Application of integration

Q: 8. The area enclosed between y= (x - 3)² + 1, the x-axis, x = 3 and x = 5 is rotated about the line…

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Q: 1. The region bounded by the curves y =7x and y=x² is rotated about the x-axis. USE THE METHOD OF…

A: Two given curves are  y=7x  (i)y=x2  (ii) The region bounded by these two curves is R and R is…

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: ind the volume generated by revolving the area enclosed by the curve x²+y²=25 about the line y-8=0.

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Q: Example 1: Determine the volume of the solid obtained by rotating the region bounded by f(x)=x² –…

A: Given function   Graph the given function using graphing calculator . Also graph x=1 and x=4…

Q: 4. A solid is obtained by rotating about the x-axis. The curve is given to be as y = 3x2 – x³. Find…

A: Let's find.

Q: 1. y = 3x - x² and y = 3-x Find the volume of the solid generated by revolving about the line x = 4…

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Q: 23. The region bounded by the curve 4y = x, the line x = 4 and the line y = 1, is rotated through…

A: Disclaimer: "Since you have asked multiple questions, we will solve the first question for you.  If…

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

A: Using disc method, volume is evaluated.

Q: EXAMPLE 3 The region bounded by the curve y = Vx, the x-axis, and the line x = 4 is revolved about…

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Q: 1. The region bounded by the curves y = 5x and y=x² is rotated about the x-axis. USE THE METHOD OF…

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Q: EXAMPLE The region between the curve y = Vx, 0 sxs 4, and the x-axis is revolved about the x-axis to…

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Q: 8. Find the volume of the solid obtained by revolving the region bounded by the graphs of y =-x cos…

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Q: Q3. The region bounded by the curve y x² and the line y 3x, is revolved about the line x = -3. Find…

A: Here i use cylindrical shell method to find out volume of rotation

Q: 4. The region bounded by the parabola y = x² and the line y = 2x in the first quadrant is revolved…

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Q: R is the region bounded above by the graph of f(x) = 6e-x² and below by the x-axis over the interval…

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Q: Example 7: Find the volume of the solid whose base is bounded by the circle x2 + y² = 4, the cross…

A: Question 7: To find the volume of the solid whose area is bounded by the circle  x2+ y2 = 4, the…

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

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Q: 2. Find the volume V of the solid of revolution generated by revolving the region bounded by the…

A: Given that y=2x-2x2  Find the volume about x-axis Also the given line is x=2

Q: Q-1: Find the volume of the formed that generated by revolving the region bounded by the graphs y =…

A: given y=x-1y=x-12 graph of the region

Q: Q3. The region bounded by the curve y = x² and the line y = 3x, is revolved about the line x = -3.…

A: We will find this using formula. As per our guidelines we are supposed to answer only one question.…

Q: P2: Calculate the volume of solid of revolution when the region bounded by y = √√x + 4 and x - 2y +…

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Q: a) Find the points of intersection of the curves y = -3x? and y = 2x2 - 80. b) Find the Volume of…

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Q: 2. Find the volume of the solid form by the region bounded by the curves y = 16 – x, y = 3x + 12,…

A: Volume of solid is 686.96

Q: Consider a thin plate of constant density d lying in the regionbounded by the graphs of y = √x and x…

A: First find the intersection points of the given curve, by equating the y of both curves…