Server Not Reachable. *This may be due to your internet connection or the nubtrek server is offline.*

Thought-Process to Discover Knowledge

Welcome to **nub****trek**.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue

Welcome to **nub****trek**.

The content is presented in small-focused learning units to enable you to

think,

figure-out, &

learn.

**Just keep tapping** (or clicking) on the content to continue in the trail and learn. continue

The content is presented in small-focused learning units to enable you to

think,

figure-out, &

learn.

To make best use of nubtrek, understand what is available.

nubtrek is designed to explain mathematics and science for young readers. Every topic consists of four sections.

nub,

trek,

jogger,

exercise.

This captures the small-core of concept in simple-plain English. The objective is to make the learner to think about. continue

Trekking is bit hard, requiring one to sweat and exert. The benefits of taking the steps are awesome. In the trek, concepts are explained with exploratory questions and your thinking process is honed step by step. continue

This captures the essence of learning and helps one to review at a later point. The reference is available in pdf document too. This is designed to be viewed in a smart-phone screen. continue

This part does not have much content as of now. Over time, when resources are available, this section will have curated and exam-prep focused questions to test your knowledge. continue

Voice

Voice

Home

» Understanding Algebra of Integrals*how integral applies to a function given as algebraic operations of several functions*

→ addition and subtraction

→ product and division

→ function-of-function

→ parametric form of function

*plain and simple summary*

nub

*plain and simple summary*

nub

dummy

*simple steps to build the foundation*

trek

*simple steps to build the foundation*

trek

You are learning the free content, however do shake hands with a coffee to show appreciation.

*To stop this message from appearing, please choose an option and make a payment.*

In this page, what is algebra of integrals and conditions under which it is applicable are discussed.

Starting on learning "Understanding Algebra of Integration". In this page, what is algebra of integrals and conditions under which it is applicable are discussed.

What does the title "Algebra of Integration" or "Algebra of Integrals" mean?

- Properties to find integrals of functions given as algebraic operations of several functions
- application of integration

The answer is "Properties to find integrals of functions given as algebraic operations of several functions"

The mathematical operations are

• addition and subtraction `u(x) +- v(x)`

• multiple of a function `a u(x)`

• multiplication and division `u(x)v(x)` and `(u(x))/(v(x))`

• powers and roots `[u(x)]^n` and `[u(x)]^(1/n)`

• composite form of functions `v (u(x))`

• parametric form of functions `v=f(r) ; u=g(r)`

Given that `f(x) = u(x)***v(x)` where `***` is one of the arithmetic or function operations.

Will there be any relationship between the integrals of the functions `int u(x) dx` ; `int v(x) dx` and the integral of the result `int f(x) dx`?

Algebra of integration analyses this and provides the required knowledge.*Note: In deriving the results, the functions are assumed to be continuous and integrable at the range of interest. For specific functions at specific intervals, one must check for the continuity and the integrability before using the algebra of integrals.*

For example, consider

`u(x) = x^2`

`v(x) = sin x`

`f(x) = x^2 sin x`

From the standard results, it is known that

`int x^2 dx = x^3/3 + c` and

`int sin x dx = -cos x + c`.

What is `int x^2 sin x dx`?

In this particular example multiplication is considered. Instead of multiplication, one of the arithmetic or function operations may be considered too.

The algebra of integrals analyses this and provides the required knowledge to solve.

*comprehensive information for quick review*

Jogger

*comprehensive information for quick review*

Jogger

dummy

*practice questions to master the knowledge*

Exercise

*practice questions to master the knowledge*

Exercise

*your progress details*

Progress

*About you*

Progress

What does the title : Algebra of Integration, or, Algebra of Integrals mean.

find;given;algebraic;several

Properties to find integrals of functions given as algebraic operations of several functions

application

application of integration

The answer is "Properties to find integrals of functions given as algebraic operations of several functions"

The operations are, addition and subtraction; multiple of a function; multiplication and division ; powers and roots; composite form of function ; parametric form of functions.

Given that f of x equals u of x star v of x. Where star is one of the arithmetic, or, function operations. Will there be any relationship between the integral of the functions, integral u of x d x ; integral v of x d x, and the integral of the result integral f of x d x? Algebra of integration analyses this and provides the required knowledge.

For example, consider u of x equals x squared, v of x equals sine x , f of x equals x squared sine x. From the standard results of integrals, it is known that integral x squared = x cubed by 3 + c and integral sine x dx = negative cos x . What is integral x squared sine x dx? In this particular example multiplication is considered. Instead of multiplication, one of the arithmetic or function operations may be considered too. The algebra of integrals analyses this and provides the required knowledge to solve.