# Volume of solid

1. Dec 1, 2006

### necessary

volume of solid:(

question is; y=x and y=x^1/2 about y =1

2. Dec 1, 2006

3. Dec 1, 2006

### necessary

ok I showed my work..

I used this formula
integral Pı(outer r)^2-Pı(inner)^2

inside integral from y=0 to y=1 pi(1-y)^2 - pi(1-y^2)^2

my result is 7/6 pi..:( where am I wrong??

4. Dec 1, 2006

integrate it with respect to x. The inner radius is $$1-\sqrt{x}$$ and the outer radius is $$1- x$$.

So you have $$\int_{0}^{1} \pi((1-x)^{2}-(1-\sqrt{x})^{2}) \; dx$$

Last edited: Dec 1, 2006
5. Dec 1, 2006

### arildno

Well, your integrand is utterly wrong!
You are to rotate the VERTICAL strip $\sqrt{x}\leq{y}\leq{x}$ around y=1.
That gives you the integral:
$$V=\int_{0}^{1}\pi((1-x)^{2}-(1-\sqrt{x})^{2})dx=\pi\int_{0}^{1}(x^{2}-3x+2\sqrt{x})dx$$

6. Dec 1, 2006

### arildno

Apart from being wrongly signed, you have rotated your figure around the line x=1, rather than around y=1.