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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
A

This represents the Gaussian integral, which states that the integral of the function e−x2e^{-x^2} over the entire real line from negative infinity to positive infinity is equal to the square root of pi. This integral is widely used in statistics and probability theory.


Evaluation

Evaluation ID
978dc716-4438-45f3-8c4f-5cd536d08c5f
Created
April 23, 2024

Evaluation Rating

Binary Pass/Fail
Pass
Score
100
Additional Feedback
The submitted answer perfectly matches the expert answer and provides additional context about the significance of the Gaussian integral in statistics and probability theory.
Factual Consistency
A: the submitted answer is a subset of the expert answer and is fully consistent with it
Raw Output
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Raw Rating Output
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