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What does the following represent: ∫−∞∞e−x2 dx=π\int_{-\infty}^\infty e^{-x^2} \,dx = \sqrt{\pi}


OpenAI: GPT-3.5 Turbo 16k
PublicPass
C

This is the Gaussian integral, and it states that the integral of the function e−x2e^{-x^2} from negative infinity to positive infinity is equal to the square root of pi. This integral has many important applications in mathematics and physics, including probability theory and quantum mechanics.


Evaluation

Evaluation ID
50ce8f8a-1975-4cb9-90ae-f41bf77d3ae1
Created
April 23, 2024

Evaluation Rating

Binary Pass/Fail
Pass
Score
100
Factual Consistency
C: the submitted answer contains all the same details as the expert answer
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