Integral

Vocabulary of the equation

1. F(x)= f'(x)
2. c = constant
3. n = constant
4. $\int _{a}^{b}$ = Integrals from a to b

Definite Integral

Some equations you can remember But when you are looking at the equation you must need to know F(x)= f'(x).

1. $\int _{a}^{b}f(x)\,dx=F(b)-F(a)$
2. $\int _{a}^{b}{x^{n}}\,dx={b^{n+1} \over n+1}-{a^{n+1} \over n+1}$

Indefinite Integral

Some equations you can remember But same you must need to know F(x)= f'(x).

1. Indefinite Integral $\int f(x)\,dx=F(x)+c,$
2. sum rule of Indefinite Integral $\int [f(x)+g(x)]\,dx=\int f(x)\,dx+\int g(x)\,dx$
3. The Difference Rule $\int [f(x)-g(x)]\,dx=\int f(x)\,dx-\int g(x)\,dx$
4. Indefinite Integral $\int x^{n}\,dx={x^{n+1} \over n+1}+c$
5. Natural log rule $\int {n \over x}\,dx={ln|x^{n}|}$
6. $\int a^{x}dx={a^{x} \over \in (a)}$
7. constant(constant can be pull out in the Indefinite Integral) $\int c*f(x)dx=c\int f(x)dx$

Examples

Examples for Definite Integral

1. $\int _{a}^{b}f(x)\,dx=F(b)-F(a)$

This is the rule that we will going to used for calculating areas

Know Here are some example for you to do

Examples for Definite Integral 1

$\int _{2}^{3}8x^{3}+3x^{2}+6x\,dx$