SOLUTION: integrale from ( -inf,+inf ) for e^-(ABSOLUTE VALUE OF X ) ? CAN I GET ANY HELP ..SOON THANKS

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Question 361330: integrale from ( -inf,+inf ) for e^-(ABSOLUTE VALUE OF X ) ?
CAN I GET ANY HELP ..SOON
THANKS
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
... First break up the integral.


Note: We're using the idea that f%28x%29=abs%28x%29 is a piecewise function and for some number c which is in the interval [a,b]


... Simplify


... Now introduce limits.


... Take the antiderivative of e%5Ex to get e%5Ex. Take the antiderivative of e%5E%28-x%29 to get -e%5E%28-x%29.


... Pull the negative out of the second limit.


... Evaluate at the limits of integration.


... Evaluate e%5E0 to get 1.


... Evaluate each limit.


... Subtract.


... Subtract.