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Bookmark or Share- calculus - Is there really no way to integrate $e^{-x^2 ...$\begingroup$ @user599310, I am going to attempt some pseudo math to show it: $$ I^2 = \int e^-x^2 dx \times \int e^-x^2 dx = Area \times Area = Area^2$$ We can replace one x, with a dummy variable, move the dummy copy into the first integral to get a double integral.
- solving the integral of $e^{x^2}$ - Mathematics Stack ExchangeThe integral which you describe has no closed form which is to say that it cannot be expressed in elementary functions. For example, you can express $\int x^2 \mathrm{d}x$ in elementary functions such as $\frac{x^3}{3} +C$. However, the indefinite integral from $(-\infty,\infty)$ does exist and it is $\sqrt{\pi}$ so explicitly:
- calculus - relation between integral and summation - Mathematics Stack ...Well, the linearity just follows from the fact that you can swap integral and the sum (i.e. these two operators commute) - but an extremely important fact that the sum is a special case of an integral, and the integral is a limit of sums is not used there.
- Lebesgue integral basics - Mathematics Stack ExchangeThe Riemann integral is like picking up the coins, one-by-one, and adding the denomination of each to a running total. The Lebesgue integral is like sorting the coins by denomination first, and then getting the total by multiplying each denomination by how many you have of that denomination and then adding up those numbers.
- Newest 'integration' Questions - Mathematics Stack ExchangeFor questions about the properties of integrals. Use in conjunction with (indefinite-integral), (definite-integral), (improper-integrals) or another tag(s) that describe the type of integral being considered. This tag often goes along with the (calculus) tag.
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