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Determine the resulting volume (in cu. units) when enclosed area between the functions below are revolved around the y-axis: 𝑦=𝑥2+1, 𝑦=𝑥2, 𝑦=1 and 𝑦=4

Question

Determine the resulting volume (in cu. units) when enclosed area between the functions below are revolved around the y-axis: 𝑦=𝑥2+1, 𝑦=𝑥2, 𝑦=1 and 𝑦=4
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Solution 1

To find the volume of the solid formed by revolving the area between the curves around the y-axis, we can use the method of cylindrical shells. The formula for the volume of a cylindrical shell is V = 2π ∫ [r(h) dr] from a to b, where r is the radius and h is the height of the cylindrical shell.

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