Approximating a quarter circle of radius 10 gives areas 77.6131 by the trapezoidal rule and 78.17563 by Simpson's rule. Taking $\pi=3.14$ as exact, which rule is better and why?

1. The exact quarter-circle area is $\dfrac{\pi r^2}{4}=\dfrac{\pi(10)^2}{4}=25\pi$. 2. Trapezoidal: $25\pi=77.6131$ gives $\pi\approx 3.10$. 3. Simpson's: $25\pi=78.17563$ gives $\pi\approx 3.13$. 4. Absolute errors against $3.14$ are $|3.14-3.10|=0.04$ and $|3.14-3.13|=0.01$. 5. Simpson's error is the smaller, so it is the better approximation. Both rules used the same ten strips, so strip count cannot be the reason. _Source: NECTA ACSEE 2023 Advanced Mathematics 142/1, Question 7: Numerical Methods_