Consider a function ft for which the exact integral between

Consider a function \"f(t)\" for which the exact integral between x = 20 (=a) and x = 40 (=b) is equal to 77.068. Suppose that a MATLAB script file estimate_integral_m has been has been written to estimate this integral \"f(x)\" between x = a and x = b. Is it possible for the following reaults to be obtained? Be sure to explain why or why not. You may assume that \"f(x)\" and \"a\" and \"b\" are the same for all three cases. estimate_integral The computed value for I with \"n\" = 10 is 480.77. >> estimate_integral The computed value for I with \"n\" = 100 is 770.67. >> estimate_integral The computed value for I with \"n\" = 1000 is 670.45.

Solution

for n=10, computed integral value I may be 480.77 as we are integrating the function f from x=20 to x=40, and take n=10, that means step size is 2. so we may get less computed value I as step size is 2 (bigger value)

for n=100, computed integral value I may be 770.67  as if the function is linear, we will get exact value (with small error)

for n=1000, computed integral value I may not be 670.45, since if we take step size small, then the computed value approaches to exact value.

note: if the function is reimann integrable.