Integration is the process of finding the equation of a graph from the equation of its gradient. It is the exact inverse of differentiation.

Representing it

The integrated form of a function is represented as $\int f(x)$, or $f(x)$ when $f’(x)$ is given.

Calculating it

For simple equations

When $f’(x) = ax^n$, $f(x) = (ax^(n+1))/(n+1) + C$. 'C' represents the integration constant, which is an unknown number you must calculate using the values you are given.

For trigonometric functions

• $\int cos(x) = \sin(x)$
• $\int -sin(x) = \cos(x)$
• $\int sec^2(x) = \tan(x)$
• $\int -csc^2(x) = \cot(x)$
• $\int sec(x) * tan(x) = \sec(x)$
• $\int -csc(x) * cot(x) = \csc(x)$
• $\int 1/sqrt(1-x^2) = \arcsin(x)$
• $\int -1/sqrt(1-x^2) = \arccos(x)$
• $\int 1/(x^2 + 1) = \arctan(x)$