Simpsons rule volume washers shells about y=-1

[z37002]

Simpsons rule n=6, to approximate volume of solid obtained by rotating the region bounded by y=x^3,y=1,x=0 about line y=-1. What is the volume integral to use, and how is it put into simpsons rule form? thanks.

 

[Simon Bridge]

Welcome to PF;
Those are questions for you ... how have you attempted to answer them so far?
Hint:
State Simpson's rule
Sketch the region
Shift the origin

Have you studied solids of rotation before?

 

[z37002]

Yes, I've done both revolution of solid and simpsons, but not together? And it is the about y=-1 as opposed to on the axis that I seek help w. And if the integral I know is shells, than how do plug in x values if integral is in y's? I am not seeing this as being able to be simple discs. Though a shift of y-axis shouldn't effect x values, I still see the y=-1 as a deterrent to combining simpsons sand shells. IF another way or similar example please share.

 

[z37002]

Any advice would be good.

 

[NascentOxygen]

Any advice would be good.

Post a link to your sketch.

 

[Simon Bridge]

You know how to do solids of rotation about one of the principle axes of the coordinate system.
However, you don't know how to handle arbitrary rotations?

What you have to do is realize that the positon and orientation of the axes doesn't matter for the problem - so move to a new coordinate system where one of the principle axes lines up with the rotation axis.

You should see how to do this if you sketch the situation out.