Estimate the error in using (a) the Trapezoidal Rule and (b) Simpson's Rule with $n = 8$ when approximating the following integral.
$$\int _ { 4 } ^ { 6 } ( 6 z + 3 ) d z$$
A) The error for the Trapezoidal Rule is $0.0051$ and for Simpson's Rule it is $0.0013$.
B) The error for the Trapezoidal Rule is $0.0000$ and for Simpson's Rule it is $0.0200$.
C) The error for the Trapezoidal Rule is $0.0204$ and for Simpson's Rule it is $0.0200$.
D) The error for the Trapezoidal Rule is $0.0204$ and for Simpson's Rule it is $0.0000$.
E) The error for the Trapezoidal Rule is $0.0000$ and for Simpson's Rule it is $0.0000$.

Question

Quizplus · Accepted Answer

The integral of a linear function, such as $6z + 3$, can be exactly calculated by both the Trapezoidal Rule and Simpson's Rule, regardless of the number of intervals $n$. This means there is no approximation error for either method in this case.

Estimate the Error in Using (A) the Trapezoidal Rule and (B)