Q:

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 Integral b a f(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

Accepted Solution

A:
The left sum would be f0+f1+f2+f3The right sum would be f1+f2+f3+f4The trapezoidal rule value is:(f0+f1)/2 + (f1+f2)/2+(f2+f3)/2 +(f3+f4)/2This would put the trapezoidal rule in the middle , which makes the answer:Lower sum < Trapezoidal rule Value < Upper sum