# Calculus

posted by .

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) and the shell height as (4x-2x^2).

My final integral was 2 pi * integral from 0 to 2 of [(6-x)(4x-2x^2)]. I was just wondering if I did this correct? Thanks.

• Calculus -

Yes, your expressions for the radius and the height are correct. The expression to integrate as well. The shell method evaluates basically ∫2πr(x)h(x)dx. The limits have not been stated in the question, but I suppose they are from x=0 to x=2, as you put it.
Good work!

## Similar Questions

1. ### 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
2. ### 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
3. ### 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 a)the line x = 4
4. ### calculus

2. Let R be the region in the first quadrant bounded by the graphs of (x^2/9)+(y^2/81)=1 and 3x+y=9 . a. Set up but do not evaluate an integral representing the area of R. Express the integrand as a function of a single variable. b. …
5. ### calculus

2. Let R be the region in the first quadrant bounded by the graphs of (x^2/9)+(y^2/81)=1 and 3x+y=9 . a. Set up but do not evaluate an integral representing the area of R. Express the integrand as a function of a single variable. b. …
6. ### 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 x-axis: Y=sqrt(x+2), y=x,y=4
7. ### calculus

1. Find the area of the region bounded by f(x)=x^2 +6x+9 and g(x)=5(x+3). Show the integral used, the limits of integration and how to evaluate the integral. 2. Find the area of the region bounded by x=y^2+6, x=0 , y=-6, and y=7. Show …
8. ### 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
9. ### Math (Calculus)

Use the disc method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated line. y=x^3, y=0, x=2 a)the x-axis b)the line x=4