What is the value of the $\displaystyle \int \limits_{-\infty}^xe ^ {\large{-t^2/2}}dt$ ?
thank you for your time.
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What are the limits of integration? – Git Gud Apr 15 '13 at 05:57
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limits are from -infinity to x. – prasad Apr 15 '13 at 05:59
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3Answer can't be expressed in terms of standard functions of intro calculus. – Gerry Myerson Apr 15 '13 at 06:04
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@prasad Following up on Gerry's comment, if that came up in a problem, you're probably supposed to just leave it like that. – Git Gud Apr 15 '13 at 06:09
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You could make the change of variable, $u=\dfrac{t}{\sqrt{2}}$, to write the integral in terms of the error function, if you wanted to. – Daryl Apr 15 '13 at 06:13
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As Gerry Myerson said, you can't express this integral in terms of elementary functions. Search for "Integration in Finite Terms" to find out why.
If you want to compute the value for a particular $x$, it can be done in terms of the "erf" function.
marty cohen
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The fact that $\int_{-\infty}^{x} e^{-at^{2}} dt$ doesn't have a anti-derivative function in closed form is the reason every textbook on probability and statistics contains a table of the Gaussian or normal distribution. (Of course, in this modern age of ours, you can get on-line calculators to give you values of the definite integral for input values of $x$ by numerical computation.) – colormegone Apr 16 '13 at 22:27