Finding Volume of Solid of Revolution around Y-Axis

[lionely]

Homework Statement

Find the volume of the solid generated by rotating about the y-axis
y= 1-x³ x=0 , y=0

I tried sketching the graph of y= 1-x^3 then tried to find the volume from y=1 to y=0.

if x^3 = 1-y
x= (1-y)^1/3
so x²= (1-y)^2/3

∏∫x²δy

=> ∏∫(1-y)^2/3.dy = ∏[ -3/5(1-y)^(5/3)]

I did that for y=1 to y=0.
But I can't get the right answer.

I got 0pi
but the answer should be 3pi/5

 

[eumyang]

It would be helpful if you told us what answer you got and what answer you are supposed to get.

 

[lionely]

I edited it

 

[eumyang]

The antiderivative looks right, so it looks like the error is in substituting the y = 1 and y = 0. Double check your work.

 

[lionely]

omg I'm so stupid I didn't do the one for 0, because most times when it's 0 I ignore it. Bad a habit. I got 3/5pi now

 

[haruspex]

∏[ -3/5(1-y)^(5/3)]

I did that for y=1 to y=0.

What did you get for each bound (y=0, y=1)?

 

[lionely]

I got it now!