I'm asked to find the average value of a function, on an interval [5,15] given its rate of change (derivative):
$ f(v)= 2*e^-0.4v-e^-0.12v $
When I integrate this function, I get: $(-2/0.4)*e^-0.4v +(1/0.12)*e^-0.12v+C$ (I was given some values so I also know that C=20 in the original function)
Since I believe this to be the primitive function F(v), should I integrate it again in order to evaluate it for 15 and 5? Or should I just plug in the values [5,15] (and multiply by 1/15-5) this same function?
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$\begingroup$The average value of a function $f$ in the interval $[a,b]$ is given by $$\frac{1}{b-a}\int_a^b f(x)dx.$$
So you need to find $$f(v):=\int e^{-0.4v}-e^{-0.12v}dv$$ and then calculate $$\frac{1}{10}\int_5^{15} f(v)dv.$$
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