Sketch the region bounded by the curves y = x^2 and y = 2 then set up the integral needed to find the volume of the solid generated by revolving this region about the x-axis using the shell method. a) integral_0^2 2 pi y^3/2 dy b) integral_0^2 4 pi/y^3/2 dy c) integral_0^2 2 pi y^2 dy d) integral_-Squareroot 2^Squareroot 2 pi y^3/2 dy e) integral_-Squareroot 2^Squareroot 2 4 pi y^3/2 dy

Option b

Step-by-step explanation:

given that a region is bounded by the curves

It is rotated about x axis

We are to use shell method

Region picture is enclosed

We are to use shell method

Due to symmetry we can find form 0 to 2 and double it.

Here limits for y are from  0 to 2

The variable x can be written as

A(y) = area =

Volume =

Hence option b is right

volume of the solid

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step-by-step explanation:

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