QUESTION 1 (GAUSSIAN INTEGRAL) The Gaussian integral
\int_(-\infty )^(\infty ) e^(-x^(2))dx=\sqrt(\pi )
It has great importance in various areas such as statistics. But how is this function integrated to obtain the value of
\sqrt(\pi )^(')
? Find some useful change of variable that allows you to transform this integral into a more comfortable form.
I^(2)=\int_(-\infty )^(\infty ) \int_(-\infty )^(\infty ) e^(-(x^(2)+y^(2)))dxdy
Solve the double integral and end up finding the value of the Gaussian integral.

Question

QUESTION 1 (GAUSSIAN INTEGRAL) The Gaussian integral

\int_(-\infty )^(\infty ) e^(-x^(2))dx=\sqrt(\pi )

It has great importance in various areas such as statistics. But how is this function integrated to obtain the value of

\sqrt(\pi )^(')

? Find some useful change of variable that allows you to transform this integral into a more comfortable form.

I^(2)=\int_(-\infty )^(\infty ) \int_(-\infty )^(\infty ) e^(-(x^(2)+y^(2)))dxdy

Solve the double integral and end up finding the value of the Gaussian integral.

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Expert Answer to - QUESTION 1 (GAUSSIAN INTEGRAL) The Gaussian integral  int_(- infty )^( infty ) e^(-x^(2))dx= sqrt( p

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Solution for - QUESTION 1 (GAUSSIAN INTEGRAL) The Gaussian integral  int_(- infty )^( infty ) e^(-x^(2))dx= sqrt( p

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This an additional answer to - QUESTION 1 (GAUSSIAN INTEGRAL) The Gaussian integral  int_(- infty )^( infty ) e^(-x^(2))dx= sqrt( p

(Solved): QUESTION 1 (GAUSSIAN INTEGRAL) The Gaussian integral \int_(-\infty )^(\infty ) e^(-x^(2))dx=\sqrt(\p ...