# Simpson's Rule question, which I hate!

1. Feb 22, 2006

### Hootenanny

Staff Emeritus
The question is use simpson's rule with five ordinates to find an approximation for
$$\int_{0}^{4} cos \left[ e^{\frac{1}{2} x} \right] dx$$
Here are my figures (working in radians)
$$y_0 = 0.540302305$$
$$y_1 = -0.077846103$$
$$y_2 = -0.911733914$$
$$y_3 = -0.228658946$$
$$y_4 = 0.448356241$$
Plugging these into the formula for Simpson's rule gives:
$$\int_{0}^{4} cos \left[ e^{\frac{1}{2} x} \right] dx \approx \frac{1}{3} \left[ (0.540302305 + 0.448356241) + 4(-0.077846103 -0.228658946) + 2(0.448356241 -0.911733914) \right]$$
This gives - 0.388....... when the answer in the textbook is -0.6869. I know its alot of number crunching but any help would be appreciated.

2. Feb 22, 2006

### becz-

I don't really know what you are doing there..

if you just go

1/3 (y0 + 4y1 + 2y2 + 4y3 + y4) it works properly

3. Feb 22, 2006

### Hootenanny

Staff Emeritus
I was using the formula we have been given, you've just expanded the brackets. I've obviously just punched the numbers into my calculator wrong. Thank's.