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CSS Applied Mathematics QUESTION #1305
Question 1
The Trapezoidal Rule for \(n\) equally spaced points with step size \(h\) is:
  • \(\dfrac{h}{2}(y_0+2y_1+\cdots+2y_{n-1}+y_n)\)✔️
  • \(\dfrac{h}{3}(y_0+4y_1+2y_2+\cdots+y_n)\)
  • \(h(y_0+y_1+\cdots+y_n)\)
  • \(\dfrac{h}{2}(y_0+y_n)\)
Correct Answer Explanation
The Trapezoidal Rule approximates \(\int_a^b f(x)\,dx\approx\dfrac{h}{2}[f(x_0)+2f(x_1)+2f(x_2)+\cdots+2f(x_{n-1})+f(x_n)]\). This gives the first and last function values weight 1 and all interior values weight 2.