Math Help Forum - View Single Post

Boris B · #12 April 19th, 2008, 10:51 PM

I think I've been using this formula wrong. Do we ever actually take the derivative of the thing we originally turned into the derivative? This would be clearer if the example hadn't used a base e exponent; I think that is what may be screwing me up.

I tried to take the antiderivative of:
$f(x) = \frac{2.5(200)^{2.5}}{x^{3.5}}$
First I decided that I could take the derivative of $x^{3.5}$ . Since it was in the denominator first, I had to turned into a $x^{-3.5}$ and make it part of the numerator. Then I multiplied that by $2.5(200)^{2.5}$
$2.5(200)^{2.5} \cdot x^{-3.5} - \int ...$

For the other side of the integral, I took the derivative of $2.5(200)^{2.5}$ , which, lacking a variable, is 1. That left $x^{3.5}$ , which integrates to $\frac{x^{4.5}}{4.5}$

That leaves me with
$2.5(200)^{2.5} \cdot x^{-3.5} - \frac{x^{4.5}}{4.5} =$
$1,414,213 x^{-3.5} - \frac{x^{4.5}}{4.5} =$

The definite integrals I take are all quite preposterous (e.g. 5.02 billion minus negative infinity), implying my antiderivative is wrong. (My end goal is to find the difference of the 70th and 30th percentiles of X; I assume I'll need the antiderivative for this but I haven't quite worked out the endgame.)