Quadrature

It is a Numerical tool that is used to find the area under a curve without performing a symbolic integration. Some of the basic Quadratures are as follows.

1. Left rectangle rule

$$Q(f)=f(a)(b-a)$$

2. Right rectangle rule

$$Q(f)=f(b)(b-a)$$

3. Midpoint rule

$$Q(f)=f\left(\frac{a+b}{2}\right)(b-a)$$

4. Trapezoid rule

$$Q(f)=\frac{f(a)+f(b)}{2}\left(b-a\right)$$

5. Kepler / Simpson’s Rule

$$Q(f)=\frac{b-a}{6}\left[f(a)+4f\left(\frac{a+b}{2}\right)+f(b)\right]$$