I'm trying to integrate

.

Y is a random variable, K is a constant.

I think I need to do this because it is a density function and I need a distribution function.

I decide to give it a shot without U substituting, because I don't know if need it and I certainly haven't got the hang of it yet. (I know I have to U substitute if there is anything in the equation other than X, but I gather I can take out coefficients like k, so I'm not sure about this one.)

I decided to let 1-y = A. So:

Moving from the antiderivative to the definite integral is where it goes bad. I don't think I've ever gotten a negative answer to a definite integral, but on the interval (0, 0.4) I get -0.184k.

Assuming I do need to use U substitution, does anyone have any suggestions on pointers for how to use it? The book I'm using is getting worn with my re-reading the pair of brief sentences which are supposed to explain it....