1. ## double integral

integral from 1 to 2 and integral from 1 to 3 of e^(-(x+y))

Is there any reference I can go to to refresh my calculus.
It's been over 10years since I took my Calculus

Judi

2. Originally Posted by Judi
integral from 1 to 2 and integral from 1 to 3 of e^(-(x+y))

Is there any reference I can go to to refresh my calculus.
It's been over 10years since I took my Calculus

Judi
By the rules of exponents
e^{-x-y} = e^{-x} * e^{-y}
so you can write your integral as separate integrations over x and y:
Int[e^{-x-y} dx dy] = Int[e^{-x} dx] * Int[e^{-y} dy]

and

Int[e^{-x} dx] = -e^x (over the appropriate limits)

As I don't know which limits go with which variable I can't help any further, but I suspect you can take it from here.

(I'll let someone else handle the question about references.)

-Dan

3. Thank you!

4. Originally Posted by topsquark
By the rules of exponents
e^{-x-y} = e^{-x} * e^{-y}
so you can write your integral as separate integrations over x and y:
Int[e^{-x-y} dx dy] = Int[e^{-x} dx] * Int[e^{-y} dy]

and

Int[e^{-x} dx] = -e^x (over the appropriate limits)

As I don't know which limits go with which variable I can't help any further, but I suspect you can take it from here.

(I'll let someone else handle the question about references.)

-Dan
As the integrand is separable into a product of two functions one containing
only one of the variables and the other the remaining variable, and these
two functions are the same (except for the name of the variable) it does
not matter which set of limits go with which variable the integral is the same
which ever way they are allocated to the variables.

RonL

5. Originally Posted by Judi
in

Is there any reference I can go to to refresh my calculus.
It's been over 10years since I took my Calculus
There are plenty of online resources for calculus one I like is William Chen's
lecture notes, which you can find here, but a google search for "calculus notes"
will give you more links that you can shake a stick at.

If it you want a good text book, I like Morris Klein's Calculus which has the
advantages of being cheap and good.

RonL

6. Originally Posted by CaptainBlack
As the integrand is separable into a product of two functions one containing
only one of the variables and the other the remaining variable, and these
two functions are the same (except for the name of the variable) it does
not matter which set of limits go with which variable the integral is the same
which ever way they are allocated to the variables.

RonL
I was just trying to be general. Okay! Okay! I didn't notice that.

-Dan

7. Thank you guys!