Question
Asked Nov 28, 2019
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Find the volume when the region bounded by the y=√(3x) and y=√(3−x) is rotated about the x axis.

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Expert Answer

Step 1

To calculate the volume of the region bounded by the given curves when rotated around x-axis.

-У3x
у 3
у%3Dу3—х
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-У3x у 3 у%3Dу3—х

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Step 2

To find the volume of revolution, we will use the Shell method. The region bounded by the curves when rotated about x-axis, it gives the solid shown as below:

(0.75, 1.5)
y=v3x
y=3-x
(0.75,-1.5)
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(0.75, 1.5) y=v3x y=3-x (0.75,-1.5)

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Step 3

Since the region bounded between the curves is easy to integrate with respect to the vari...

y 3r. On squaring both sides, we get
y23x
And
y 3-x.On squaring both sides, we get
-x
y2 3-x
x3-y
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y 3r. On squaring both sides, we get y23x And y 3-x.On squaring both sides, we get -x y2 3-x x3-y

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Tagged in

Math

Calculus

Integration