Q$3(7$ points$)$

Consider the function $f(x)=si{n}^3(5x).$ We will compare several approximation methods for ${\displaystyle \underset{0}{\overset{}{}}}f(x)dx$ using a step size of $h=\frac{}{6}.$

a$)$ Using a computer or calculator, estimate ${\displaystyle \underset{0}{\overset{}{}}}f(x)dx$ using left endpoint, midpoint, and trapezoid approximation methods.

b$)$ Calculate the true value of ${\displaystyle \underset{0}{\overset{}{}}}f(x)dx,$ and compare with the approximations from the left endpoint, midpoint, and trapezoid methods. Which one was the best approximation at this step size?