Word Count : 323

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We need to determine the minimum number of intervals \( n \) required to approximate the integral \[ I = \int_{0}^{1} e^{-x^2} \, dx \] using the trapezoidal rule with an accuracy of \[ \frac{1}{2} \times 10^{-4} = 5 \times 10^{-5}. \] ### Step 1: Trapezoidal Rule Error Formula The error bound for the trapezoidal rule is given by: \[ E_T = -\frac{(b-a)^3}{12n^2} f''(\xi) \] for some \( \xi \) in \( [a, b] \). This gives an approximation of ______ __________ ________ _______ __________ ________ _____ _________ ___ ___ ___ ________.
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