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The branch of mathematics that deals with integrals, especially the methods of ascertaining indefinite integrals and applying them to the solution of differential equations and the determining of areas, volumes, and lengths.


In this section we make the table of immediate integrals available to all. It is an indispensable resource for integral calculus when studying mathematical analysis.

Table of Integrals


Quick Navigation: Basic Rules of Differentiation



It is an exclusive e-Learning Blog that has been dedicated to help keen learn students to boost their knowledge in different subjects.

Derivatives and Anti-derivatives

The derivative of a function is one of the basic concepts of mathematics. Together with the integral, derivative occupies a central place in calculus. The process of finding the derivative is called differentiation. The inverse operation for differentiation is called integration and you can find integration using integral calculator.

The derivative of a function at some point characterizes the rate of change of the function at this point. We can estimate the rate of change by calculating the ratio of change of the function Δy to the change of the independent variable Δx. In the definition of derivative, this ratio is considered in the limit as Δx → 0. Let us turn to a more rigorous formulation.


The chart above shows to differentiate and integrate the most common functions. There are, Integration reverses differentiation, returning the function to its original state, up to a constant C.

Credit: math24
It is an exclusive e-Learning Blog that has been dedicated to help keen learn students to boost their knowledge in different subjects.

Basic Rules of Integration



It is an exclusive e-Learning Blog that has been dedicated to help keen learn students to boost their knowledge in different subjects.
The derivative of" is also written d/dx. So d/dx f(x) and f’(x) both mean "The derivative of f(x)".

Basic Rules of Differentiation


Rule-1 related Example: What is d/dx (x5)?

Solution:
The question is asking "What is the derivative of x5 "?
Where, n=5
We know, d/dx (xn) = nxn-1
Now, d/dx (x5) = 5x5−1 = 5x4
(In other words the derivative of x5 is 5x4)

Quick Navigation: Basic Rules of Integration