Posted by Anthony on Saturday, December 8, 2007 at 11:49pm.
I still do not understand how to solve the following problem. Please show stepbystep.
x = Integral (0 to v) dv/(q^2v^2) where q = constant
the answer is > x = 1/2q ln (q+v/qv)
1) Where 1/2q came from?
2) Where ln came from? Is there a formula for it?
Please help!!!!!!!

Math  drwls, Sunday, December 9, 2007 at 12:46am
I explained this yesterday. You use the method of partial fractions, to rewrite
1/(q^2v^2) as the sum of terms with
(q+v)and (qv) in the denominator. When you integrate those two separate terms, you get the difference of two log terms.
Look up the method in your text or verify the integal in a table of integrals.
[1/(2q)] is a factor appears when the method of partial fractions is correctly applied.

Math  drwls, Sunday, December 9, 2007 at 4:51am
"ln" is term that designates the natural (base e) logarithm of whatever follows. ln x is the integral of dx/x
ln (q+v) is the integral of dv/(q+v), with q being a constant. When you do the integration, you get the ln(q+v)  ln (qv). Using the rules of logarithms, this can be written ln[(q+v)/(qv)]. The 1/2q factor comes from the step of converting 1/(q^2v^2) to two partial fractions.
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