Question

calendar BAU BUZEB BAU Library 3-9) Cal... Overview Plans Resources Status and follow-up Participants M Suppose that f(x) is a non-negative and continuous function on the interval [a, b]. The following method (illustrated in the below figure) is a well-known method to approximate the total area underneath the curve of f(x) on the given interval: b-a • Divide the interval (a, b) into 5 subintervals each of width 5 . For each 1sis 5, choose any arbitrary point in the ith subinterval. • Thus, the total area underneath the curve of f(x) can be approximated by: RCS;4,62,65,6,cs) = "" [sc)+(0) + f(c) + f(c) + f(c)). y

Answer 1

The method is applicable if f(t) is a non-negative and Continuous function on the interval [a, b] (A) f(1) = lnn Interval Cl, 10 In interval (1,10] fon) is a non-negative and continuous function, so statement is drue. >10 21:10 [True sentence ®) fima CSCHE I sina Interval [7 / 7 Slzo 2 for Us a non- negative and continuous femelton , so statement is true. 22 Az 아니엇 [True sentence 3 1600) (4,0) fim = =√gon Interval [og] frana ugon is a non-negative and continuary function , so statement is true (True sentence d) fem) = 5 Interval Co, v3] function ferns is not defined at r= 13, so function is not om the interval Co, 13]. Statement is fulse. 3-218 continuous function (false sentence] f(x) = seen Interval [0, 73 2 function fen) is non-negative and Continuous fumetion, so stalement is true. [True sentence MB

Tuy f(x) = en Interval .c-s,s] 2 function fons is non-negative and continuous funetion, so statement Is faue, [True sentenie H=-5 2=5