Mathematics - Definite Integration Question with Solution | TestHub

Suppose we define the definite integral using the following formula:

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

For a more accurate result, for $c\in (a,b)$, we have:

$$F(c)=\frac{c-a}{2}(f(a)+f(c))+\frac{b-c}{2}(f(b)+f(c))$$

When $c=\frac{a+b}{2}$, we get:

$${\int }_a^{b}f(x)dx=\frac{b-a}{4}(f(a)+f(b)+2f(c))$$