How to calculate the area under a Weibull curve

Alright it took me some time to figure out. I am using a survival function: S(t) = exp(−αtγ)
scale = exp(log-scale)
γ = 1/Scale
α =exp(−(Intercept)γ)

This is not the same as the probability density function.

I guess i am only missing the information on the beta parameter to use the WEIBULL.DIST() function.
Any chance you could tell me how I can derive beta?