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Asked Dec 7, 2019
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Let S be the solid obtained by rotating the region bounded by the curves y = x(x – 1)² and y = 0 about the y-axis. If you sketch the given region, you'll see that it
can be awkward to find the volume V of S by slicing (the disk/washer method). Use cylindrical shells to find V .
Volume =
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Let S be the solid obtained by rotating the region bounded by the curves y = x(x – 1)² and y = 0 about the y-axis. If you sketch the given region, you'll see that it can be awkward to find the volume V of S by slicing (the disk/washer method). Use cylindrical shells to find V . Volume =

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Expert Answer

Step 1

Given,

           Let S be the solid obtained by rotating the region bounded by the curves y = x (x – 1)² and y = 0 about the y-axis.

Graph of Curve is given below.

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у%3 х (х — 1)2 -02 (0, 0) 0.6 0.8 02 0.4 (1, 0) -0.2 From the graph, we can see that lower limit is x = 0 and upper limit is x = 1.

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Step 2

Now, using the cylindric...

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The radius for the typical shell is just x. The height is x(x – 1)². : V = 2n x(x(x – 1)²) dx = 2n x?(x – 1)² dx 2n x* – 2x³ + x² dx 2x4 = 2n 4 3 15

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Tagged in
MathCalculus

Integration