the are bounded by the parabola ay=x², the x-axis, and the line x=b is revolved about the y-axis. Find the volume generated.

Q: Find the volume generated if the area bounded by curve y = x^2 and the line y = 2x + 3 is revolved…

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Q: Let M be the region in the first quadrant bounded by the graph of y=3x+2, the graph of y=x+2, and…

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Q: Show by integration that the volume V of a right circular cylinder with base radius r and height h…

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Q: If the area of the curve y = sinx from x = 0 to x = π is revolved about the y=axis i, what is the…

A: The given curve is: y=sin x      from  x=0  to  x=π

Q: If the area bounded by y = x² and y = 2 – x² is revolved about the x – axis and a vertical…

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Q: Find the volume generated by rotating the given region about the specified line. R, about AB

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Q: Suppose that R is the finite region bounded by y = 1, y = x + 5, x = 0, and z = 4. Find the exact…

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Q: Find the volume under the surface formed by f(x, y) = xy2 over the rectangle %3D 0 Sa<2 and 0 SyS 3.…

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Q: Given an area D bounded by curve y = 4x−x^2, line x+y = 6, and y-axis. Find the volume if the area D…

A: We are given an area D bounded by curve y = 4x - x2, line x + y = 6, and y-axis. We need to find the…

Q: 3. Find the volume generated by revolving the area bounded by the parabola y² = 8x and its latus…

A: Given

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Q: Find the volume generated by the area bounded by the parabola x=√ay , and the line y=b that is…

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Q: Determine the volume if the area common with y^2 - 3x + 7y = 8 and x^2 - 4x +3 = y^2 is revolved…

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Q: Show that the volume generated by revolving the region in the first quadrant bounded by the…

A: Solution is below.

Q: What is the volume, br^3, of the rotating body obtained by rotating the graph of the function y = Vx…

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Q: ind the volume of the solid whose base is a circular disk of radius R, centered at the origin and…

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Q: p3y 8–x²-y² dzdxdy 0.

A: We solve triple integration using ordinary method

Q: Given the volume R of the solid bounded by the graphs of z = 9 – y?, x +z = 9, x = 0 and z = 0.

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Q: Suppose that RR is the finite region bounded by  y=x, y=x+4, x=0, and x=2. Find the exact value of…

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Q: Find the volume generated when the given curve is rotated about the x-axis from x=o to x=1. * 3 y =…

A: Given is the curve y=(x+4)3, 0≤x≤1 The objective is to find the volume when this curve is rotated…

Q: 1. Calculate the volume bounded by y = x², y = 0 and x = 2 rotated about the specified line, using…

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Q: Let A be the area in the first quadrant bounded by the y-axis, the line y=5 x, and the line y=2…

A: Suppose a region is enclosed by two curves, y=fx and y=gx. To calculate the volume of the region…

Q: Determine the volume if the area common with y^2-3x+7y=8 and x^2-4x+3=y^2 is revolved about the…

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Q: Find the surface area of the volume generated when of y = x3, on the interval [0, 1], is revolved…

A: We have to find the surface area of the volume generated by the curve by rotating about the y axis.

Q: Given that R is the area bounded by the curve y = 9 – x^2 and y = 5. Calculate the volume of the…

A: Given that R is the area bounded by the curve y=9−x2 and y=5. We have to calculate the volume of the…

Q: Find the volume generated by revolving about the x-axis, the area bounded by the line 2x + 4y = 4,…

A: I am attaching image so that you understand each and every step.

Q: the area bounded by the parabola ay= x², the x-axis, and the line x= b is revolved about the x-axis.…

A: Value of 'a' may be positive or negative, taking |b| as absolute value of b.

Q: Find the volume generated if the area bounded by curve y=x^2 and the line y=2x + 3 is revolved about…

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Q: The area bounded by the parabola ay = x², the x-axis, and the line x = b is revolved about the…

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Q: For the area bounded by the given curves Area enclosed by 9x^2 + 4y^2 = 36. Find the volume…

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Q: 1. Find the volume generated by revolving the first quadrant area bounded by the parabola y? 8x and…

A: Proceed as shown ....

Q: Find the volume of the solid whose base is bounded by the circle x2 + y2 = 9 and whose cross…

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Q: Find the volume generated by rotating the given region about the specified line. R, about BC

A: In this question, we find the volume by rotating the region R1 about the line BC.

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Q: Find the volume generated by revolving the area bounded by y² – 4y – 4x + 4 = 0 and x = 1 about the…

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Q: Suppose that R is the finite region bounded by y = x, y = x + 1, x = 0, and x = 2. Find the exact…

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Q: Suppose that R is the finite region bounded by y = x, y = x + 2, a = 0, and a 3. Find the exact…

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Q: Find the volume generated if the area bounded by curve y = x^2 and the line y = 2x+ 3 is revolved…

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Q: Find the surface area of the volume generated when the following curves revolve around the x-axis. y…

A: To solve the following problem of surface area of the volume generated.

Q: Suppose that R is the finite region bounded by y = x, y = x + 5, x = 0, and x = = 4. Find the exact…

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Q: Find the volume.

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Q: Suppose that R is the finite region bounded by y = x, y = x + 1, x = 0, and x = 5. Find the exact…

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Q: Find the surface area of the volume generated when the following curves revolve around the given…

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Q: Find the volume generated by revolving the area bounded by y² – 4y – 4x + 4 = 0 and x 1 %3| about…

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Q: Given the volume R of the solid bounded by the graphs of z = 9 – y?, x + z = 9, x = 0 and z = 0.

A: Volume bounded by region, using triple integral

Q: Given that the area R is limited by the curve y = x + 1, y = −x + 1 and the line y = α, 0 ≤ α ≤ 1.…

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Q: If we have a half-circle of radius r centered at 0, prove thatthe volume of the sphere resulting…

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Q: Solve the following. 1. Find the volume generated by revolving the first-quadrant area bounded by…

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