1. use the shell method to write and evaluate the definite internal that represents the volume...

1. use the shell method to write and evaluate the definite internal that represents the volume of the solid generated by revolving the plan region about the x-axis. x+y^2=4

2. use the shell method find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the given line. y=(x)^1/2. y=0 x=4. about the line x=6

Solutions

Expert Solution

1. The parabola can be sketched as below

Using the method of shells,

For the given curve,

Hence, the integral works out to

2. The region is again a parabola, and this time the axis of rotation is parallel to the Y axis. The region to be rotated in shown in orange in the sketch below

Again using the method of shells and keeping in mind that the axis is now x = 6 so radius will be (6 - x),

milcah answered 2 years ago

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