Use the error formula to estimate the error in approximating the integral
$$\int _ { 3 } ^ { 6 } ( 9 x + 1 ) d x$$ with $n = 4$ using Trapezoidal Rule.
A) 3
B) 1
C) 6
D) 0
E) 9

Question

Quizplus · Accepted Answer

The error in the Trapezoidal Rule for approximating integrals is given by $-\frac{(b-a)^3}{12n^2}f''(x)$ for some $x$ in $[a, b]$, where $f''(x)$ is the second derivative of the function being integrated. For the function $f(x) = 9x + 1$, the second derivative $f''(x) = 0$. Therefore, the error in approximating the integral using the Trapezoidal Rule is 0, regardless of the number of intervals $n$.

Use the Error Formula to Estimate the Error in Approximating ∫36(9x+1)dx\int _ { 3 } ^ { 6 } ( 9 x + 1 ) d x∫36​(9x+1)dx

Use the Error Formula to Estimate the Error in Approximating $\int _ { 3 } ^ { 6 } ( 9 x + 1 ) d x$