The Impossible Integral ... you can't solve it скачать в хорошем качестве

The Impossible Integral ... you can't solve it

In this video, we solve one of the most famous integrals in mathematics—the Gaussian integral. The integral of e^(-x²) from negative infinity to positive infinity has no elementary antiderivative, yet we can still find its exact value using one of the most brilliant tricks in calculus. We'll walk through the complete proof step-by-step, showing how squaring the integral and converting to polar coordinates leads us to the beautiful result: √π. This integral is the foundation of probability theory, statistics, and appears throughout physics and engineering. Whether you're a calculus student, math enthusiast, or just curious about elegant mathematical proofs, this video will show you why the Gaussian integral is considered one of the most important and beautiful results in all of mathematics. 🔔 Subscribe for more advanced math tutorials and mind-blowing mathematical proofs! 💬 What integral should I solve next? Drop your suggestions in the comments below! 📚 Topics covered: The Gaussian integral Why e^(-x²) has no elementary antiderivative Double integrals and polar coordinates The normal distribution connection Applications in physics and statistics #Mathematics #Calculus #GaussianIntegral #Integration #MathTutorial #AdvancedMath #Probability #Statistics