A continuous function on satisfies for and for

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

Problem

A continuous function hh on [0,9][0,9] satisfies h′′(x)>0h''(x)>0 for 0<x<40<x<4 and h′′(x)<0h''(x)<0 for 4<x<94<x<9. Using three equal subintervals of length 3, both a midpoint sum M3M_3 and a trapezoidal sum T3T_3 are computed to approximate ∫09h(x) dx\displaystyle \int_{0}^{9} h(x)\,dx. Which approximation, M3M_3 or T3T_3, is likely to be closer to the true value of the integral? Briefly justify your choice.

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