List of practice Questions

If the numerical approximation of the value of the integral \( \int_0^4 2^\alpha x \, dx \) using the Trapezoidal rule with two subintervals is 9, then the value of the real constant \( \alpha \) is \(\underline{\hspace{2cm}}\) (round off to one decimal place).

Evaluate \(\int_{1}^{5} x^2 dx\) using 4 equal intervals by trapezoidal rule and Simpson's 1/3 rule, and compute the absolute difference (round to 2 decimals).