Volume of revolution: y=x^2, x-axis, x= 1: rotated about....

[mattflint50]

Can you please tell me if I did this problem right. The question was, the region bounded by y=x^2 , the x axis and x=1 is rotated about the x axis and x=1. Find the volume generated.


First I chose the shells method.
I said that v=the integral from 0 to 1 of (y)(1-y^(.5))
So v=the integral from 0 to 1 of (y-y^(3/2))
So v= (-pi (y^2) (4 radical(y)-5))/5

For an answer I got pi/5.

Is this right?

Thank you

 

[galactus]

Looks good.

Try the washer method now.

\(\displaystyle \L\\{\pi}\int_{0}^{1}(x^{4})dx\)

Do you get the same thing?.

Now, can you revolve it about x=1 too?.