Joshua F.

asked • 04/01/19

Need Help Understanding

Function f(x) is positive, increasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the upper sum, lower sum, and trapezoidal rule approximations for the value of the integral from a to b of f of x dx. Which one of the following statements is true?

Lower sum < Trapezoidal rule Value < Upper sum

Lower sum < Upper sum < Trapezoidal rule value

Trapezoidal rule < Lower sum < Upper sum

Cannot be determined without the x-values for the partitions

K.J. P.

tutor
Draw a picture. Since f(x) is positive, increasing, and concave up, it looks like y = x^2 from 1 to 2. Use that sort of curve as your example and it should be clear what's going on.
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04/01/19

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Stephen X. answered • 04/02/19

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