Posted by **carlton** on Wednesday, May 2, 2012 at 7:31pm.

Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis:

Y=sqrt(x+2), y=x,y=4

- calculus -
**Reiny**, Wednesday, May 2, 2012 at 9:50pm
A rough sketch and some quick easy algebra shows that the curve intersects the lines at (2,2) and (14,4)

and the two straight lines intersect at (4,4)

so in 2 parts ....

V = π∫( x^2 - (x+2) ) dx from 2 to 4 + π∫(16 - (x+2))dx from 4 to 14

= π [(1/3)x^3 - (1/2)x^2 - 2x] from 2 to 4 + π[ 16x - (1/2)x^2 - 2x] from 4 to 14

I will let you do the arithmetic

## Answer this Question

## Related Questions

- calculus - Use the shell method to set up and evaluate the integral that gives ...
- Math (Calculus) - Use the shell method to set up and evaluate the integral that ...
- Calculus - Use the shell method to set up, but do not evaluate, an integral ...
- calculus - Use the shell method to find the volume of the solid generated by ...
- calculus - Use the disk or the shell method to find the volume of the solid ...
- Math (Calculus) - Use the shell method to find the volume of the solid generated...
- Calculus check - The functions f and g are given by f(x)=sqrt(x^3) and g(x)=16-...
- Calculus - Volume by Integration - Find the volume of the solid generated by ...
- Calculus AP - Let R be the region in the first quadrant bounded by the graph y=3...
- Calculus - Volume By Integration - Find the volume of the solid generated by ...