Question

Related to the numerical method, the formula by the trapezoidal rule is _________.

Answer 1

The trapezoidal rule works by approximating the region under the graph of the function $f\left(x\right)$ as a trapezoid and calculating its area.

The trapezoidal rule is to find the exact value of a definite integral using a numerical method. This rule is mainly based on the Newton-Cotes formula which states that one can find the exact value of the integral as an $n^{th}$ order polynomial.

When $n=1$ according to Trapezoidal rule, the area under the linear polynomial is stated as,

${\int }_a^{b}f\left(x\right)dx=(b-a)\left(\frac{f\left(a\right)+f\left(b\right)}{2}\right)$