What Is the Integral of e^-(constant)x^2?

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In summary, the integral of e^-(constant)x^2 is (sqrt(pi))/sqrt(constant). The constant in the integral of e^-(constant)x^2 can be solved for by setting the integral equal to a known value and solving the resulting equation. This integral cannot be evaluated using basic integration techniques and requires more advanced techniques. The constant in the integral affects the shape of the curve by determining its width and height, and it can be used to solve real-world problems in various fields such as physics and engineering.
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Kristen
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Need the integral of e^-(constant)x^2...don't want to use guass integral trick
 
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  • #2
Here is a thread that discusses various ways for evaluating Gaussian integrals,

http://www.nrich.maths.org/askedNRICH/edited/2171.html

but the equations may not come across on your browser.
 
  • #3
The indefinite integral cannot be expressed in simple form. Usually it is given in terms of a function called "erf", which is simply a standard form (constant=1/2) integral.
 

FAQ: What Is the Integral of e^-(constant)x^2?

What is the integral of e^-(constant)x^2?

The integral of e^-(constant)x^2 is (sqrt(pi))/sqrt(constant).

How do I solve for the constant in the integral of e^-(constant)x^2?

The constant in the integral of e^-(constant)x^2 can be solved for by setting the integral equal to a known value and solving the resulting equation.

Can the integral of e^-(constant)x^2 be evaluated using basic integration techniques?

No, the integral of e^-(constant)x^2 cannot be evaluated using basic integration techniques. It requires more advanced techniques such as substitution or integration by parts.

What is the relationship between the constant in the integral of e^-(constant)x^2 and the shape of the curve?

The constant in the integral of e^-(constant)x^2 affects the shape of the curve by determining its width and height. A larger constant will result in a narrower and taller curve, while a smaller constant will result in a wider and shorter curve.

Can the integral of e^-(constant)x^2 be used to solve real-world problems?

Yes, the integral of e^-(constant)x^2 has many applications in physics, engineering, and other fields. It can be used to model the distribution of energy, calculate probabilities, and solve differential equations.

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