Find the volume of x = y − y2, x = 0, rotated around the y-axis.

So I first found the zeroes, which were 1 and 0. Then I squared the function and got y^(2)+y^(4)-y^(6)

Then I took the integral and plugged in the 1's and 0's until I got [(1/3)+(1/5)-(1/7)]-[0].

So as my final answer, I received pi(41/105).
I don't know where I went wrong.

Question

Find the volume of x = y − y2,   x = 0, rotated around the y-axis.

So I first found the zeroes, which were 1 and 0.  Then I squared the function and got y^(2)+y^(4)-y^(6)

Then I took the integral and plugged in the 1's and 0's until I got [(1/3)+(1/5)-(1/7)]-[0].  

So as my final answer, I received pi(41/105).
I don't know where I went wrong.

ganeshie8 · Answer

again, what do you get for $(y-y^2)^2$ ?

anonymous · Answer

y^(2)+y^(4)-y^(6)
(y-y^2)(y-y^2)=(y-y^2)^2

ganeshie8 · Answer

doesn't look correct, try again

ganeshie8 · Answer

you may want to use the formula
$$(a-b)^2=a^2-2ab+b^2$$

anonymous · Answer

thanks, it's the simple stuff that stumps me

ganeshie8 · Answer

happens... yw :)

ganeshie8 · Answer

wolfram is good for double checking these https://www.wolframalpha.com/input/?i=%5Cint_0%5E1+pi*%28y-y%5E2%29%5E2+dy

anonymous · Answer

Thanks!!