Two Questions, one I'm pretty confident I've done and just want confirmation, the other I'm stuck on:

First Question:

Use Simpson's Rule, n=4, to approximate:

$\displaystyle \int^5_2 \sqrt(x-1).dx$

and find a bound on the error.

I won't bore you all with the full result:

h=3/4

k=0, x0=2, y0=2, w0=1, yw=2

k=1, x1=2.75, y1=2.658, w1=4, yw=10.583

k=2, x2=3.5, y2=3.162, w2=2, yw=6.325

k=3, x3=4.25, y3=3.605, w3=4, yw=14.422

k=4, x4=5, y4=4, w5=1, yw=4

Simpson's approximation = 3/12*37.330 = 9.332 (3dp)

Hope that's correct!

Error:

$\displaystyle f''''(x)=\frac{-15}{16}(x-1)^{\frac{-7}{2}}$

x=5, this is -0.007.

Error = (-0.007*243)/(180*256) = -0.0000386

also correct?

Okay onto the volume question I'm stuck on:

Base of a solid V is the region bounded by $\displaystyle y=x^2$ and $\displaystyle y=2-x^2$. Find the volume if V has square cross sections.

tbh, I'm really stuck on this one and haven't the foggiest!