What is the integral method for finding the mean in exponential distribution?

[kliker]

in the exponential distribution we know that

μ = 1/λ and σ = 1/λ^2

also f(x) = λ*e^-λχ

how can i find the mean (μ) using integrals?

generally what we do is this

we integrate from a point to another the x*f(x) (EX)

And the variance is EX^2-(EX)^2

but here we have no points, so how can i prove that the mean is 1/λ?

 

[gabbagabbahey]

I assume that your distribution is defined for $0\leq x<\infty$? If so, you integrate over that entire interval:

$$\mu=\int_0^{\infty}xf(x)dx$$