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danai_pa
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Please healp me
What is the solution of equation?
intregal of Ax^2*exp(-x^2/2a^2)
What is the solution of equation?
intregal of Ax^2*exp(-x^2/2a^2)
Do you want a definite or indefinite integral? The antiderivative of this function cannot be written in terms of elementry function. If you know the function erf(x) you can express the integral in terms of it (hint: integrate by parts). erf is usually defined in terms of the integral of exp(-x^2). You can also find the integral of the function over the whole real line by integrating by parts and using the fact that the whole real line integral of exp(-k x^2) isdanai_pa said:Please healp me
What is the solution of equation?
intregal of Ax^2*exp(-x^2/2a^2)
The general formula for solving integrals of this form is:
∫ Ax^2 * exp(-x^2/2a^2) dx = √(2πa^4) * A/2
The limits of integration for this integral are determined by the range of values for x that are relevant to the problem at hand. These limits can be determined by examining the context of the problem and identifying the relevant variables and their ranges.
Yes, this integral can be solved using basic integration techniques such as substitution, integration by parts, or partial fractions. However, depending on the value of a, it may also require the use of more advanced techniques such as completing the square or trigonometric substitutions.
The parameter "a" represents the standard deviation of the normal distribution that is being integrated. It affects the shape and width of the curve and can impact the difficulty of solving the integral. When a is small, the curve is narrow and tall, making it easier to solve the integral. When a is large, the curve is wider and flatter, making the integral more challenging.
This integral can be solved analytically using the formula mentioned in the first question, as long as the limits of integration and the parameter "a" are known. However, in some cases where the limits are complex or the value of a is very large, it may be more practical to use numerical methods such as Simpson's rule or the trapezoidal rule to approximate the value of the integral.