Two Questions, one I'm pretty confident I've done and just want confirmation, the other I'm stuck on:
Use Simpson's Rule, n=4, to approximate:
and find a bound on the error.
I won't bore you all with the full result:
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!
x=5, this is -0.007.
Error = (-0.007*243)/(180*256) = -0.0000386
Okay onto the volume question I'm stuck on:
Base of a solid V is the region bounded by and . Find the volume if V has square cross sections.
tbh, I'm really stuck on this one and haven't the foggiest!