The Trapezoidal Rule approximates the integral of a function by dividing the area under the curve into trapezoids.

Area=$\frac{1}{2}(a+h)h$

$f(x)=x^3+2x^2+3x+4$

$\displaystyle \int_a^b f(x)dx \approx \sum_{i=0}^{n-1} \frac{1}{2}\left( f(x_i)+f(x_{i+1}) \right) (x_{i+1}-x_i)$

Actual integral value=297.08

n=6
Sum of the areas of trapezoids=305.00
ERROR=7.92

n=11
Sum of the areas of trapezoids=299.06
ERROR=1.98

n=101
Sum of the areas of trapezoids=297.10
ERROR=0.02

As the number of trapezoids increases, the approximation of the integral becomes more accurate.