# Should be simple polynomial integral

1. May 8, 2012

### DaleSwanson

This is the end of a triple integration problem. I can get down to what seems like it should be a simple polynomial integral of a single variable. Yet I just can't get the numbers to work out.

$\int_0^5 \frac{-1}{2}x^3 + \frac{15}{2} x^2 - \frac{75}{2} x + \frac{125}{2} dx$

The indefinite integral should be:
$\frac{-1}{8}x^4 + \frac{5}{3} x^3 - \frac{75}{4} x^2 \frac{125}{2} x + C$

At 0 that should equal 0, so we only need to worry about its value at 5, which should be:
$\frac{-625}{8} + \frac{625}{3} - \frac{1875}{4} + \frac{625}{2} = \frac{-625}{24}$

However, the correct answer should be 625/8. My answer is off by a factor of -6.

I'd assume I had made a mistake getting to this point, but Wolfram Alpha confirms that the definite integral above is equal to 625/8.
http://www.wolframalpha.com/input/?i=integral+from+0+to+5+of+125%2F2-%2875+x%29%2F2%2B%2815+x^2%29%2F2-x^3%2F2

Having WA do the indefinite integral gives my result, but also gives a form with -625/8 + C, which I assume can be ignored since it's a definite integral. Either way, including the -625/8 doesn't seem to help.
http://www.wolframalpha.com/input/?i=integral++of+125%2F2-%2875+x%29%2F2%2B%2815+x^2%29%2F2-x^3%2F2

So I'm pretty lost right now as to what could be going wrong. It's possible that I'm making a simple arithmetic mistake, as I'm pretty good at doing that, but I've checked and rechecked and just keep getting -625/24.

Can anyone see my problem?

2. May 8, 2012

### hamsterman

The problem is with your second term, It should be 15/6 = 5/2, not 5/3. I didn't check if that solves the problem though.

3. May 8, 2012

### DaleSwanson

Wow, I must have integrated that 4 times and came up with 5/3 each time. WA even shows the correct answer. Don't know how I missed it repeatedly.

Thanks.

4. May 8, 2012

### Ray Vickson

You wrote $$\int \frac{15}{2} x^2 \, dx = \frac{15}{3} x^3 \:\Longleftarrow \text{False}.$$

RGV