Answer:
statement is TRUE
statement is FALSE
statement is TRUE
Step-by-step explanation:
(a)
By using the Trapezoidal Rule, the definite integral can be computed by applying linear interpolating formula on each sub interval, and then sum-up them, to get the value of the integral
So, in computing a definite integral of a linear function, the approximated value occurred by using Trapezoidal Rule is same as the area of the region. Thus, the value of the definite integral of a linear function is exact, by using the Trapezoidal Rule.
Therefore, the statement is TRUE
(b) Recollect that for each rule of both the midpoint and trapezoidal rules, the number of sub-internals, n increases by a factor of a. then the error decreases by a factor of a^2.
So, for the midpoint rule, the number of sub-intervals, n is increased by a factor of 3, then the error is decreased by a factor of 32 = 9, not 8. Therefore, the statement is FALSE
(c) Recollect that for each rule of both the midpoint and trapezoidal rules, the number of sub-internals, n increases by a factor of a. then the error decreases by a factor of a^2.
So, for the trapezoidal rule, the number of sub-internals, n is increased by a factor of 4. then the error is decreased by a factor of 42 = 16
Therefore, the statement is TRUE
.