Calculate a volume using the washer method

[nameVoid]

Homework Statement

y=x^2+1
y=9-x^2
y=-1 rotate

Homework Equations

The Attempt at a Solution

intersection
x^2+1=9-x^2=>2x^2-8=0=>2(x^2-4)=0=>x=+-2
Washer method
outer radius = 1+9-x^2=10-x^2
inner radius = 1+x^2+1=2+x^2
Area=pi((10-x^2)^2-(2+x^2)^2)=pi(100-20x^2+x^4-4-4x^2-x^4)=pi(96-24x^2)=24pi(4-x^2)
by symatrey
V=48pi Integral( 4-x^2,x,0,2)=48pi[4x-x^3/3,0,2]=48pi(8-8/3)=48pi(24-8)/3=48pi*16/3=256pi

if you can try and solve to verify please, or else if you have a membership to cramster this is problem 10 in the the chapter 6 review stewart 5e

 

[zcd]

Yes, 256pi is right. You could always try the problem by both shell and washer method to check the answer.