Question

Given \[ \int_{0}^{3} f(x)\,dx=\int_{0}^{3}(4x^2-1)\,dx \] is approximated using Simpson's \(\frac{1}{3}\) rule with \(3\) subintervals and gives \(f(0)+a+f(3)\), then \(a\) is

• A. \(0\)
• B. \(1\)
• C. \(-1\)
• D. \(8\)

Hint:

Simpson's \(\frac13\) rule is \[ \boxed{ \int_a^b f(x)\,dx \approx \frac{h}{3} \left[ f(x_0)+4f(x_1)+2f(x_2)+\cdots+4f(x_{n-1})+f(x_n) \right]. } \]

Answer 1

The Correct Option is C