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Trapezoidal and Midpoint Rule Error Relationship

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Consider the approximation of ∫131x2dx\int_{1}^{3} \frac{1}{x^2} dx with nn uniform subintervals. Let ETE_T be the error resulting from a trapezoidal sum and EME_M be the error resulting from a midpoint Riemann sum. Which of the following equations correctly relates ETE_T and EME_M?

A

E_T = 2E_M

B

E_T = -2E_M

C

E_T = -E_M/2

D

E_T = -E_M

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