calculus
posted by Ryan .
Find the volume of the solid generated by revolving about line x = 4 the region bounded by x = y  y^2 and x = y^2  3

The curves intersect at (2,1) and (3/4,3/2)
So, we want to sum up the washers with inner radius r and outer radius R
Int pi*(R^2  r^2)[1,3/2] dy
where
R = y  y^2 + 4
r = y^2  3 + 4 = y^2 + 1
R^2  r^2
= (y^2  y^3 + 4y  y^3 + y^4  4y^2 + 4y  4y^2 + 16)  (y^4 + 2y^2 + 1)
= 2y^3  9y^2 + 8y + 15
V = pi*(1/2 y^4  3y^3 + 4y^2 + 15y)[1,3/2]
= 1085pi/96
Respond to this Question
Similar Questions

Calculus
"Find the volume of the solid generated by revolving the region bounded by the graphs of the given equations about the indicated lines: y = 2x^2 y = 0 x = 2 About the line y = 8" 
calculus
Consider the region bounded by the parabola y=x^2 and the line y=16 . (a) What is the volume of the solid generated when revolving this region about the line y=16 ? 
calculus
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line x = 6. y = 6 − x y = 0 y = 5 x = 0 
Calculus
Find the volume of the solid generated by revolving the following region about the given axis. The region in the first quadrant bounded by the curve y=x^2, below by the xaxis, and on the right by the line x=1, about the line x=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 a)the line x = 4 
Calculus
Find the volume or the solid generated by revolving around the region bounded by the graphs of the equations about line x=6. xy=6, y=2, y=6, and x=6 
Calculus
Find the volume of the solid generated by revolving the region bounded by the line y=5x+6 and the parabola y=x^2 about the following lines: a) the line x=6 b) the line x=1 c)the x axis d) the line y=36 Thanks! 
calculus
determine the volume of the solid of revolution generated by revolving the region bounded by y=x^3x^5, y=0, x=0 and x=1 about the line x=3 
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 … 
Calculus
Can you please check to see if these answers are correct?