(i)[3]
Apply the trapezium rule with $3$ intervals to obtain an approximation for $I$, and give the result correct to $3$ decimal places.
(ii)[5]
When $x$ is small, $(1 + 3x^2)^{-2} \approx 1 + ax^2 + bx^4$. Determine the values of the constants $a$ and $b$. Hence, by evaluating $\int_{0}^{0.3} (1 + ax^2 + bx^4) \, dx$, find a second approximation to $I$, giving the answer correct to $3$ decimal places.