Approximating an Integral

Calculus Level 3

For all cubic polynomials f(x)f(x), what positive value of kk makes the following statement true?

∫−11f(x)dx=f(−k)+f(k)\int_{-1}^{1}f(x)dx = f(-k) + f(k)

Bonus question: What is this method of approximation known as?

Andrew Ellinor by Andrew Ellinor
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