Solution

Past exam of the mathematics course of the University of Cambridge / 2001 / iii / Paper 32 / 6 / i / Solution

Past exam of the mathematics course of the University of Cambridge / 2001 / iii / Paper 42 / 1 / Solution

Past exam of the mathematics course of the University of Cambridge / 2002 / ib / Paper 1 / 7B / Solution

Past exam of the mathematics course of the University of Cambridge / 2002 / ib / Paper 2 / 18D / c / Solution

Past exam of the mathematics course of the University of Cambridge / 2002 / iii / Paper 25 / 2 / Solution

Past exam of the mathematics course of the University of Cambridge / 2002 / iii / Paper 48 / 1 / b / Solution

Past exam of the mathematics course of the University of Cambridge / 2002 / iii / Paper 51 / 2 / Solution

Past exam of the mathematics course of the University of Cambridge / 2002 / iii / Paper 51 / 3 / Solution

Past exam of the mathematics course of the University of Cambridge / 2002 / iii / Paper 65 / 2 / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2002 / iii / Paper 65 / 2 / d / Solution

Past exam of the mathematics course of the University of Cambridge / 2002 / iii / Paper 65 / 3 / Solution

Past exam of the mathematics course of the University of Cambridge / 2002 / iii / Paper 69 / 2 / b / Solution

Past exam of the mathematics course of the University of Cambridge / 2002 / iii / Paper 69 / 4 / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2003 / iii / Paper 22 / 3 / Solution

Past exam of the mathematics course of the University of Cambridge / 2003 / iii / Paper 29 / 4 / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2003 / iii / Paper 41 / 6 / iii / Solution

Past exam of the mathematics course of the University of Cambridge / 2003 / iii / Paper 48 / 1 / Solution

Past exam of the mathematics course of the University of Cambridge / 2003 / iii / Paper 48 / 2 / c / Solution

Past exam of the mathematics course of the University of Cambridge / 2004 / ib / Paper 2 / 19D / Solution

Past exam of the mathematics course of the University of Cambridge / 2004 / iii / Paper 30 / 6 / c / Solution

{c}
{title2=$\int_{-\infty}^{\infty}e^{-x^2}\,dx=\sqrt\pi$}
{wiki}

The Gaussian integral is
$$
\int_{-\infty}^{\infty}e^{-ax^2}\,dx=\sqrt{\frac\pi a},
\qquad a>0.
$$
Squaring the integral and changing to polar coordinates proves the formula.


Gaussian integral

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