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) (Show Source): You can put this solution on YOUR website!
}dx+\int_{0}^{\infty} e^{-(x)}dx)
... First break up the integral.
Note: We're using the idea that is a piecewise function and dx=\int_{a}^{c}f(x)dx+\int_{c}^{b}f(x)dx)
for some number c which is in the interval [a,b]
... Simplify
... Now introduce limits.
+\lim_{b\rightarrow \infty}\left(\left. -e^{-x} \right|_{0}^{b}\right))
... Take the antiderivative of to get . Take the antiderivative of to get .
-\lim_{b\rightarrow \infty}\left(\left. e^{-x} \right|_{0}^{b}\right))
... Pull the negative out of the second limit.
-\lim_{b\rightarrow \infty}\left(e^{-b}-e^0\right))
... Evaluate at the limits of integration.
-\lim_{b\rightarrow \infty}\left(e^{-b}-1\right))
... Evaluate to get 1.
-\left(0-1\right))
... Evaluate each limit.
)
... Subtract.
... Subtract.
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