Engineering Application:

In a civil engineering context, the load distribution on a beam is modeled by $f(x)=5x^2+10($in $k\frac{N}{m})$ over a length of $6$ meters.

a$)$ Use the trapezoidal rule with $n=3$ subintervals to estimate the total load on the beam.

b$)$ Use Simpson's rule with $n=4$ subintervals to improve the estimate.

Which method gives a more accurate result, and why?