# Math

Find the volume of the solid obtained by rotating the region enclosed by y=x^2, y=6x about the line x=0using the method of disks or washers.

1. 👍
2. 👎
3. 👁
1. the curves intersect at (0,0) and (6,36)

using washers of thickness dx, we have

v = ∫[0,6] π(R^2-r^2) dx
where R=6x and r=x^2
v = ∫[0,6] π(36x^2-x^4) dx = 5184π/5

To check, try using shells of thickness dy:

v = ∫[0,36] 2πrh dy
where r=y and h=√y-y/6
v = ∫[0,36] 2πy(√y-y/6) dy = 5184π/5

1. 👍
2. 👎
2. How did u get all of that

1. 👍
2. 👎

## Similar Questions

1. ### Calculus

Find the volume of the solid obtained by rotating the region bounded by y= x^(1/3), and y= x about the line y=1

2. ### calculus

Consider the solid obtained by rotating the region bounded by the given curves about the x-axis. y = 9 - 9x^2 , y = 0 Find the volume V of this solid. Sketch the region, the solid, and a typical disk or washer. Any help or tips

3. ### calculus

Find the volume of the solid obtained by rotating the region bounded by y=x and y=√x about the line x=2. Volume =

4. ### Calculus

Find the volume of the solid obtained by rotating the region bounded by y= x^2, y=0, and x=3 about the x-axis.

1. ### calculus

Find the volume of the solid formed by rotating the region enclosed by y=e2x+1, y=0, x=0, x=0.9 about the y-axis.

2. ### Calculus

a) Find the volume formed by rotating the region enclosed by x = 6y and y^3 = x with y greater than, equal to 0 about the y-axis. b) Find the volume of the solid obtained by rotating the region bounded by y = 4x^2, x = 1, and y =

3. ### calculus 2

Find the volume of the solid formed by rotating the region enclosed by y=e^(5x) , \ y=0, \ x=0, \ x=0.8 around the y-axis Please help, i have been attempting these problems for a couple of days

4. ### cal

Find the volume of the solid obtained by rotating the region bounded by y=4x^2,x=1,y=0 about the x-axis.

1. ### Calculus

Find the volume of the solid formed by rotating the region enclosed by y=e^(5x)+(3), y=0, x=0, x=0.8 about the x-axis.

2. ### calculus

Find the volume of the solid obtained by rotating the region bounded by the curves y = x^8, y = 1 about the line y = 5.

3. ### Calculus :)

Find the volume of the solid formed by rotating the region enclosed by y=e^(3x)+2, y=0, x=0, x=0.4 about the x-axis.

4. ### Calc2

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = x2, y = 1; about y = 6