# calculus

posted by .

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 -

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

## Similar Questions

1. ### Calculus

Use the shell method to set up, but do not evaluate, an integral representing the volume of the solid generated by revolving the region bounded by the graphs of y=x^2 and y=4x-x^2 about the line x=6. I had the shell radius as (6-x) …
2. ### calculus

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 y-axis. y = 6x y = 18 x = 0
3. ### calculus

Use the shell method to find the volume of the solid generated by revolving the plane region about the line x = 9. y = 7x − x2 y = 0
4. ### calculus

Use the disk or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about each given line. y = x3 y = 0 x = 3 the x-axis,the y-axis,and the line x = 4
5. ### Math (Calculus)

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 y-axis. y=4-x^2, y=0
6. ### Integral calculus

Use the cylindrical shell method to find the volume of the solid generated by revolving the area bounded by the given curves (x-3)^2 + y^2 = 9, about y-axis.
7. ### Calculus

I would like to know if my answers are correct: Disclaimer: We are allowed to keep our answers in formula form 1. Use the washer method to find the volume of the solid that is generated by rotating the plane region bounded by y=x^2 …
8. ### Calculus

Hello, I would like to make sure the answers to these questions are correct. 1. Using the shell method, what is the volume of a solid that is generated by rotating the region by y = x^2 and x = y^2 about the x axis. My Work: r = y …
9. ### Calculus

Can you please check to see if these answers are correct?
10. ### Math

Let A denote the portion of the curve y = sqrt(x) that is between the lines x = 1 and x = 4. 1) Set up, don't evaluate, 2 integrals, one in the variable x and one in the variable y, for the length of A. My Work: for x: integral[4,1] …

More Similar Questions