Posted by **Claire ** on Thursday, May 9, 2013 at 4:59pm.

Let R be the region between the graph of y=x3 and the x-axis, and between x=0 and x=1.

Compute the volume of the region obtained by revolving R around the y-axis

- MATH Calculus Homework -
**Steve**, Thursday, May 9, 2013 at 5:06pm
with discs (washers),

v = ∫[0,1] π (R^2-r^2) dy

where r=x and R=1

v = π∫[0,1] (1 - y^(2/3)) dy

= π (y - 3/5 y^(5/3)) [0,1]

= 2/5 π

with shells,

v = ∫[0,1] 2π rh dx

where r=x and h=y

v = 2π∫[0,1] x*x^3 dx

= 2π (1/5 x^5) [0,1]

= 2/5 π

- MATH Calculus Homework -
**Claire **, Thursday, May 9, 2013 at 5:18pm
First off, thank you answering my question.

I just have one question. So does it matter which method we use?

I am just trying to find a better way of understanding this problem from a visual perspective.

- MATH Calculus Homework -
**Steve**, Thursday, May 9, 2013 at 5:36pm
generally it doesn't matter. It depends on whether it is easier to express y as a function of x, or vice-versa. For example if y=e^x + 4(x^2-1) then it's pretty tough to come up with y^{-1}

In this case, it was easy.

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