For on the interval

MATHEMATICS · Subjective · A Level · Mathematics · Integration · Integration

Problem

For f(x)=ln⁡xf(x)=\ln x on the interval [1,3][1,3], consider the midpoint approximation M4M_4 and the trapezoidal approximation T4T_4, each using 4 equal subintervals. Which of these two approximations yields a value greater than the exact integral ∫13ln⁡x dx\displaystyle \int_{1}^{3} \ln x\,dx? State "M4M_4" or "T4T_4" and provide a one-sentence justification based on the shape of ff.

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