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 (b)∫(a) f(x)dx

Question

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 (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

Steve · Answer

so, have you tried drawing such a curve and trying them out? How about y=x^2 where 0 <= a <= b