I need more help with this 1/(g-(k/m)v^2) dv?
I need to make a paper explaining how to solve this integral I need to factor fractions and end with a hyperbolic trig function. I will apreciate any help thanks.
- Dr DLv 71 decade agoFavorite Answer
Essentially you want to write the integral as:
(m/k)*dv / [ mg/k - v^2]
And replace mg/k with a^2.
The easiest method is to get the hyperbolic trig function directly from the integration.
Use the substitution
x = a*tanhθ
dx = a*sech^2 θ
a^2 - x^2 = a^2 * (1 - tanh^2 θ) = a^2 * sech^2 θ
So the integral of dx / (a^2 - x^2) becomes
integral of (1/a) dθ
which gives you (1/a) θ = (1/a) * tanh^-1 (x/a)
Now you just need to replace a with sqrt(mg/k) and x with v.
If you wish to integrate using partial fractions, then convert to hyperbolic trig, check out the links below where I answered very similar questions in the past.Source(s): http://answers.yahoo.com/question/index;_ylt=AliVf... http://answers.yahoo.com/question/index;_ylt=Ao1HY...