Integral Calculus

Concept of Integration
Integration is the inverse function of a derivative. Hence it is also called as anti-derivative.

Indefinite Integration
Integration without limits or intervals is called as indefinite integration. A constant is always generated in this case. The main challenge of integration is to simplify the given expression (integrand) and bring it into a suitable form, so that it can b integrated using standard formulae.

Substitution Method
If the derivative of one part of equation exists in another part of equation (numerator or denominator ) then we use the substitution method.

Integration by Parts
∫u.v dx = u ∫v dx - ∫ {du/dx (∫v dx)} dx

Integration Factor
For a differential equation of the form dy/dx + Py = Q

Integration Factor = e∫pdx

Definite Integration
Integration with limits or intervals is called as definite integration.

NOTE : If substitution method is to be used for definite integration, then the limits have to be changed according to the substitution made.

Properties of Definite Integration

 * 1) 0∫a f(x) dx = 0∫a f(a-x) dx

Application of Definite Integration
Integration can be used to multiply two quantities if the relation between them is known.

Tips and Tricks
1) u.v. shortcut :- Coming Soon

2) You can differentiate the options one by one to reach the qustion.