# Find the value for p<0?

dan
Please, can anyone help me here with this problem??

Q) Determine for what values of

element p is a member of set R, int[exp(px)]dx ; where
upper lim=infinity , lower lim=0

converges and find its value in those cases?

so far:

I got the anti-derivative of the integrand is exp(px)/p.

For the integral to exist, you must have p<0, in which case the
value is -1/p.

The integrand increases without bound for p>0, and for p=0, it is constant, again leading to an unbounded result for the value.

This is where I'm lost, how do you find the value for p<0?

Can anyone verify what I have done and help me solve this problem.

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HallsofIvy
Homework Helper
This is where I'm lost, how do you find the value for p<0?[/QUOTE}

Uhhh, didn't you just say:
For the integral to exist, you must have p<0, in which case the
value is -1/p.
?

In any case, the problem does not ask you to find the value of the integral- it only asks you to determine for what VALUES OF p the integral exists- you've already done that! (0f course, to show that your answer is correct, it is good to actually display the value: again, you've already done that!)

If I were really hard-nosed (and I AM!) I might point out that there is one error here: the anti-derivative of exp(px)= exp(px)/p only for p NOT equal to 0.

If p= 0, what is exp(px)? What is it's anti-derivative? Can that be evaluated between 0 and infinity?