A calculus problem by Joel Yip

Calculus Level 3

What is ∫ − ∞ ∞ e − x 2 d x \int _{ -\infty }^{ \infty }{ { e }^{ -{ x }^{ 2 } } } \, dx to two decimal places.


The answer is 1.77.

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Joel Yip by Joel Yip , 21, Singapore

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1 solution

Isaac Buckley
Jun 6, 2015

This is called the Gaussian integral .

It can be evaluated with a clever trick using polar coodinates.

The exact value of this is π \sqrt{\pi}

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