?Estimate the numerical value of \(\int_{0}^{\infty} e^{-x^{2}} d x\) by writing it as
Chapter 7, Problem 84(choose chapter or problem)
Estimate the numerical value of \(\int_{0}^{\infty} e^{-x^{2}} d x\) by writing it as the sum of \(\int_{0}^{4} e^{-x^{2}} d x\)and \(\int_{4}^{\infty} e^{-x^{2}} d x\). Approximate the first integral by using Simpson's Rule with \(n=8\) and show that the second integral is smaller than\(\int_{4}^{\infty} e^{-4 x} d x\), which is less than \(0.0000001\).
Equation Transcription:
Text Transcription:
integral _0 ^infinity e^-x^2 dx
integral _0 ^4 e^-x^2 dx
integral _4 ^infinity e^-x^2 dx
n=8
integral _4 ^infinity e^-4x dx
0.0000001
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