let f(x,t)=xe^(-xt).show that the integral I(x)=∫f(x,t)dt (integration from 0 to infinite)exists for all x>=0 . is x->I(x) continuous on [0,infinite)
what should i use here to prove the integral exist ???can someone give me the detail expanlation???
let f(x,t)=xe^(-xt).show that the integral I(x)=∫f(x,t)dt (integration from 0 to infinite)exists for all x>=0 . is x->I(x) continuous on [0,infinite) what should i use here to prove the integral exist ???can someone give me the detail expanlation???
thank you,then the limit is 1 so the integral exists,but how about the continuous part, for now x->I(x) ,I(X)=1 it seems ,it is continuous?? i am not sure
thank you,then the limit is 1 so the integral exists,but how about the continuous part, for now x->I(x) ,I(X)=1 it seems ,it is continuous?? i am not sure
Frankly, I have the same question about .
We know that . But I have no idea how it fits into the question.