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The integral below represent the volume of a solid. Describe the solid....

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pensivegal | (Level 1) Honors

Posted September 13, 2013 at 2:36 AM via web

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The integral below represent the volume of a solid. Describe the solid.

`int_0^1(2pix^9)dx`

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted September 13, 2013 at 10:49 AM (Answer #1)

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The problem provides the definite integral `int_0^1 (2pix^9)dx` that helps you to evaluate the volume of a solid.

You should compare the given integral to the formula that helps you to evaluate the volume of a solid obtained by rotating around y axis the region under the curve `f(x) = y` , from a to b, using method of cylindrical shells, such that:

`V = int_a^b 2pi*x*f(x)dx`

You may write the given integral, such that:

`V = int_0^1 (2pix)*(x^8)dx`

Comparing the formula and the given integral, yields:

`f(x) = y = x^8`

`a = 0, b = 1`

The problem requests for you to identify what is the solid described by the given integral.

Hence, the solid requested is obtained by revolving the region `0 <= y <= x^8, 0 <= x <= 1` , around y axis.

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