Integration is one of the basic operations of Calculus which serves as a tool to solve various mathematical problems. Integral calculus also helps in solving problems of physics which involve arbitrary shapes, length of a curve volume of cube etc. Integration is thought of as the inverse process of differentiation, which is another major branch of Calculus. Integral calculus is induced by the problem of defining and calculating the area of the section bounded by the graph of functions. Integration is also referred to as finding a function when its derivative is given.

Integration is introduced in the higher classes i.e. Class XI & XII. It is one of the most important topics in the class XII Mathematics. There is a whole bunch of formulae students need to know and remember to solve problems related to integral calculus.

Notation

The symbol for Integral is a long, styled and slim ‘S’. After the integral symbol, we put the integrand f(x) i.e. the function we want to find the integral of. The function is symbolised with a small letter styled version of ‘f’. dx differential of variable the x is added after the integrand, it indicates that the variable of integration is x.

## List of Integral Formulas

The list of Integral Formulas are given below:

• ∫ 1 dx = x + C
• ∫ a dx = ax+ C
• ∫ xdx = ((xn+1)/(n+1))+C ; n≠1
• ∫ sin x dx = – cos x + C
• ∫ cos x dx = sin x + C
• ∫ secdx = tan x + C
• ∫ cscdx = -cot x + C
• ∫ sec x (tan x) dx = sec x + C
• ∫ csc x ( cot x) dx = – csc x + C
• ∫ (1/x) dx = ln |x| + C
• ∫ edx = ex+ C
• ∫ adx = (ax/ln a) + C ; a>0,  a≠1

Some other Integration Formulas are:

## Classification of Integral Formulas

The above listed integral formulas are classified based on the following functions:

• Rational functions
• Irrational functions
• Trigonometric functions
• Inverse trigonometric functions
• Hyperbolic functions
• Inverse hyperbolic functions
• Exponential functions
• Logarithmic functions
• Gaussian function

## Solve Using Integral Formulas

1. Calculate ∫ 5x4 dx

2. Find ∫x1+2x−−−−−√dx

3. Solve∫1×2+6x+25dx