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Mar 22, 2011 · In both problems below, find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the given lines. 1) y=sqrt(x), y=0, x=4 a: the x-axis b: the y-axis c: the line x=4 d: the line x=6 2) y=x^2, y=4x-x^2 a: the x-axis b: the line y=6 I was gone for a day in calculus and I missed this new material.

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Find the volume of the solid generated by revolving the region bounded by the graph of y = x, y = 0, x = 0 and x = 2.(see figure below). Solution to Example 2. Figure 6. volume of a solid of revolution generated by the rotation of a semi circle around x axis. The graph of y = √(r 2 - x 2) is shown above...

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Area between curves. Volume of solid of revolution.

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Find the volume of the solid generated by revolving the region between the y-axis and the curve x = ( 2/y) , 1 ≤ y ≤ 4, about the y-axis. Solution: Volume = ∫ y = c d A (x) dx = ∫ y = c d π [R (y)] 2 dy = ∫ y = 1 4 π [R (y)] 2 dy = ∫ y = 1 4 π [2 / y] 2 dy = ∫ y = 1 4 π [y] − 2 dy = 3 π 4. Originally Answered: Find the volume of the solid generated by revolving the ellipse x^2/a^2+y^2/b^2=1,about the y-axis (or minor axis? Consider a curve rotated about y-axis. If we want to find volume (or surface area), consider a disc of differential width d y at some height y. The radius for this disc is x = g (y).

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Solution for Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y = e−3x , y = 0, x = 0, x…

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By integration, find the volume of the solid generated by revolving the triangular region with vertices (0, 0), (b, 0), (0, h) about a. the x-axis. b. the y-axis. theory and Applications 53. the volume of a torus The disk x2 + y2 … a2 is revolved about the line x = b (b 7 a) to generate a solid shaped like a doughnut and called a torus ...

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