calculus
posted by Tina .
Consider the solid obtained by rotating the region bounded by the given curves about the xaxis.
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 would be greatly appreciated; not sure how to work it :/

The curve intersects the xaxis at (1,0) and (1,0).
Volume = π[integral] y^2 dx from 1 to 1
or by symmetry
= 2π[integral] (99x^2)^2 dx from 0 to 1
= 2π[integral] (81  162x^2 + 81x^4) dx from 0 to 1
= 2π(81x  54x^3 + (81/5)x^5) from 0 to 1
= 2π(81  54 + 81/5  0)
= 432π/5 
khalid
Respond to this Question
Similar Questions

calculus
Consider the solid obtained by rotating the region bounded by the given curves about the xaxis. y = 6 x^6 , y = 6 x , x >= 0 Find the volume V of this solid. 
calculus
Consider the solid obtained by rotating the region bounded by the given curves about the line x = 6. y = sqrt(x), y = x Find the volume V of this solid. 
calculus
Consider the solid obtained by rotating the region bounded by the given curves about the xaxis. y=6x^5, y=6x, x>or equal to 0 Find the volume V of this solid. 
calculus
Consider the solid obtained by rotating the region bounded by the given curves about the line x = 4. x= 4y^2 , x = 4 Find the volume V of this solid. 
CALCULUS 2
Consider the solid obtained by rotating the region bounded by the given curves about the line x = 1. y = x, y = 0, x = 4, x = 6 Find the volume V of this solid 
Calculus II
Consider the solid obtained by rotating the region bounded by the given curves about the yaxis. y = ln x, y = 4, y = 5, x = 0 Find the volume V of this solid. Help!!! Thank you in advance :( 
calculus
Sketch the region bounded by the curves y = x^2, y = x^4. 1) Find the area of the region enclosed by the two curves; 2) Find the volume of the solid obtained by rotating the above region about the xaxis; 3) Find the volume of the … 
calculus
use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the xaxis. sketch the region and a typical shell. x=1+y^2, x=0, y=1, y=2 
Calculus I don't understand
Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = 10 x and y = 5 x^2 about y =0 Find the volume of the solid obtained by rotating the region bounded by y=8 x^2, x … 
Calculus Help Please Urgent!!!
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 5x^2, y = 5x, x ≥ 0; about the xaxis V = ?