Integral of exponential distribution from zero to infinity

[cooper607]

Homework Statement

here's a problem from my assignment

let integral p(x)dx=Ae^-(x/a) dx...(1)
find value of A, that makes integral p(x)dx=1;
and
find mean x so that integral x*p(x)dx=a...2)

Homework Equations

now
to solve the first one i found out A to be (-1/a*e^(x/a))
but when i am integrating the two i can not find that value 1...please tell me if my value of A is ok or not...
and for the second problem how can i integrate those three components all together?
what is the formula, please notify here...
thanks in advance

The Attempt at a Solution

A to be (-1/a*e^(x/a))

 

[tiny-tim]

hi cooper607!

you mean $[Ae^{-x/a}]_0^{infty}\ =\ 1$

… to solve the first one i found out A to be (-1/a*e^(x/a))

A is supposed to be a constant, how can it be a function of x ?

 

[dimension10]

Homework Statement

here's a problem from my assignment

let integral p(x)dx=Ae^-(x/a) dx...(1)
find value of A, that makes integral p(x)dx=1;
and
find mean x so that integral x*p(x)dx=a...2)

Homework Equations

now
to solve the first one i found out A to be (-1/a*e^(x/a))
but when i am integrating the two i can not find that value 1...please tell me if my value of A is ok or not...
and for the second problem how can i integrate those three components all together?
what is the formula, please notify here...
thanks in advance

The Attempt at a Solution

A to be (-1/a*e^(x/a))

No, its not ok. How is it even a value in the first place?

 

[Ray Vickson]

Homework Statement

here's a problem from my assignment

let integral p(x)dx=Ae^-(x/a) dx...(1)
find value of A, that makes integral p(x)dx=1;
and
find mean x so that integral x*p(x)dx=a...2)

Homework Equations

now
to solve the first one i found out A to be (-1/a*e^(x/a))
but when i am integrating the two i can not find that value 1...please tell me if my value of A is ok or not...
and for the second problem how can i integrate those three components all together?
what is the formula, please notify here...
thanks in advance

The Attempt at a Solution

A to be (-1/a*e^(x/a))

Are A and a supposed to be constants? If so, then why would you equate A to (-1/a*e^(x/a))?

Let me ask a more fundamental question: have you studied integration? Both of the questions you ask are simple integration problems from introductory calculus. However, if you have not yet had that material, it would be understandable that you are having problems.

RGV

 

[HallsofIvy]

The title of this thread says that the integral is from 0 to infinity. Did you not evaluate the anti-derivative at those values?