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For all cubic polynomials f(x)f(x)f(x), what positive value of kkk makes the following statement true?
∫−11f(x)dx=f(−k)+f(k)\int_{-1}^{1}f(x)dx = f(-k) + f(k)∫−11f(x)dx=f(−k)+f(k)
Bonus question: What is this method of approximation known as?
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