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) $