# MATH

posted by .

what is the integration of e^-|x| from negative infinity to x ?

• MATH -

since |x| = -x for x < 0.
∫[-∞,x] e^-|t| dt
= ∫[-∞,x] e^t dt if x < 0
= e^t

So, for x>=0,
∫[-∞,x] e^-|t| dt
= ∫[-∞,0] e^t dt + ∫[0,x] e^-t dt
= 1 + (1-e^-x)
= 2 - e^-x

• MATH -

What if we have .. integration of xe^(|x|) dx from negative infinity to x.

• MATH -

No idea. Do it the way I did, but you have to use integration by parts. If you get stuck, show how far you got.

You should wind up with

-(x+1)e^-x for x<0
(x-1)e^x for x>=0

## Similar Questions

1. ### Integration of exponents with absolute values

I cannot for the life of me figure this out. Please help me. How do I integrate the function f(x) = 0.1 * e ^ (-0.2 * |x|) from neg. Infinity to pos. Infinity?
2. ### college math

find the integral of x^2 e^-xdx with the limits of negative infinity to zero. so far, I have, lim as t approaches negative infinity of (-e^-x [x(x+2) + 2] from 0 to t does this converge or diverge?
3. ### Algebra

What is the answer? I came up with C. is this correct?
4. ### Calculus

Find the horizontal asymptote of f(x)=e^x - x lim x->infinity (e^x)-x= infinity when it's going towards infinity, shouldn't it equal to negative infinity, since 0-infinity = - infinity lim x-> -infinity (e^x)-x= infinity
5. ### Math

The function f(x)=(x-1)/(x-4)*sqrt(x+2) is negative for x in... a. (1,4) b. (-infinity, 4) c. (-infinity, 1) d. (4, infinity)
6. ### MATH

I have been trying to do this problem for a couple of days but i cant seem to get the answer. Any help would be greatly appreciated. For each of the following forms determine whether the following limit type is indeterminate, always …
7. ### Please check my Caclulus

1. Find all intervals on which the graph of y=(x^2+1)/x^2 is concave upward. A. (negative infinity, infinity) B. (negative infinity, -1) U (1, infinity) C. (negative infinity, 0) U (0, infinity) D. (1, infinity) E. none of these I …
8. ### Math

lim as x approaches negative infinity (3x^5 + 6x + - 3) / (8x^4 + 10) a. Does Not Exist b. 0 c. -3/8 d. 3/8 I solved this and got negative infinity as the answer, but none of the answers are listed above. I finally chose Choice C, …
9. ### Math

lim as x approaches negative infinity (3x^5 + 6x + - 3) / (8x^4 + 10) a. Does Not Exist b. 0 c. -3/8 d. 3/8 I solved this and got negative infinity as the answer, but none of the answers are listed above. I finally chose Choice C, …
10. ### Math (Limits)

lim ln(y-1) y->1+ The answer is negative infinity but how do I show the logic of proving that it's negative infinity?

More Similar Questions