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

Application Scenario of Integrals

» cause-effect relation in quantities.

» effect is the "aggregate-of-change" of cause

→ eg: displacement is "aggregate-of-change" of speed

*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, the application scenario of integrals is explained with examples.

Starting on learning "Application Scenario of Integrals". In this page, the application scenario of integrals is explained with examples.

This part of the title is repeated from the first part of differential calculus. This helps to understand the cause-effect relationship in the context of "aggregate-of-change".

Which one in the following is a measurement?

- predecessor of `7` is `6`
- length of a pen is `10`cm

The answer is " Length of a pen is `10` centimeters".

A pen can be used to write `30` pages. How many pages one can write with `4` pens?

- `4xx30`
- `120`
- both the above

Answer is "both the above".

A pen can be used to write `30` pages.

In this "number of pen" is a *cause* and "write a number of pages" is an *effect*.

This is an example of *cause and effect pair*.

Can you identify a cause-effect pair in the following?

- Volume of Paint and painted area
- Number of tickets sold and the money collected in the sale
- speed of a car and distance covered in an hour
- all the above

The answer is "all the above".

2 liter of paint is required to paint 3 square meter. If 14 liter paint is available, how much area can be painted?

- `14 xx 3/2`
- `14 xx 2/3`

The answer is "`14 xx 3/2`"

• The "area painted" is the effect.

• The "volume of paint" is the cause.

• The cause-effect relation is defined by a function involving multiplication by a constant.

`text(area) = text(volume) xx 3/2`.

Everyday, a hotel sends a worker to buy eggs from market. The eggs are priced at `1` coin each and the worker charges `5` coins for the travel to buy eggs. How many coins are to be given to buy `120` eggs?

- `120` coins
- `125` coins

The answer is "`125` coins".

• The "coins" is the effect.

• The "number of eggs" is the cause.

• The cause-effect relation is defined by a function involving addition of a constant.

`text(coins) =` ` text(number of eggs)` `xx text( price per egg)` ` + 5`

A car is moving in a straight line at constant speed. It is at a distance `10`m at `20`sec and at a distance `20`m at `25`sec. The "effect" distance is given and the "cause" speed is to be computed. What is the speed?

- speed `=(20m-10m)/(25sec-20sec)`
- speed cannot be computed as only the distance traveled is given

The answer is "speed `=(20m-10m)/(25sec-20sec)`".

• The distance traveled is the effect.

• The speed is cause.

• The cause-effect relation is defined by a function involving *rate of change*.

`text(speed) = (text(speed2) - text(speed1))/(text(time2)-text(time1))`

A car is moving in a straight line at constant speed. It has a velocity of `2` m/sec for first `3` seconds and `4` m/sec for the next `1` sec. What is the distance traveled in the `4` seconds?

- `=2m//sec xx 3 sec` `quad + 4m//sec xx 1 sec`
- distance cannot be computed as the speed is only given

The answer is "`=2m//sec xx 3 sec` `quad + 4m//sec xx 1 sec`"

• The distance traveled is the effect.

• The speed is cause.

• The cause-effect relation is defined by a function involving *aggregate of change*.

`text(distance) = text(speed1) xx text(time1)``quad + text(speed2) xx text(time2)`

From the examples, it is understood that, Definition of function as an expression involves

• addition and subtraction

• multiplication and division

• exponents and roots

Apart from these arithmetic operations, quantities may be related by "**rate of change**" and "**aggregate of change**". These two topics are covered in differential and integral calculus respectively. *In this topic, the "aggregate of change" is explained.*

*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

This part of the title is repeated from the first part of differential calculus. This helps to understand the cause-effect relationship in the context of "aggregate-of-change".

Which one in the following is a measurement?

predecessor;7;6;seven;six

predecessor of 7 is 6

length;pen;centi;meter;centimeter;10;ten

length of a pen is 10 centimeter

The answer is length of a pen is 10 centimeter

A pen can be used to write 30 pages. How many pages one can write with 4 pens?

4;30;times

4 times 30

120;20

one hundred and twenty

both;above

both the above

Answer is "both the above".

A pen can be used to write 30 pages.;; In this "number of pen" is a cause and "write a number of pages" is an effect. This is an example of cause and effect pair.

Can you identify a cause-effect pair in the following?

volume;paint;area

Volume of Paint and painted area

sold;tickets;money;collected

Number of tickets sold and the money collected in the sale

speed;car;distance;covered

speed of a car and distance covered in an hour

all;above

all the above

The answer is "all the above".

2 liter of paint is required to paint 3 square meter. If 14 liter paint is available, how much area can be painted?

3 by 2; three by two;by 3; 3 by; by two; three by; 3 buy 2; three buy two;buy 2; 3 buy; buy two; three buy

14 times 3 by 2

2 by 3; two by three;by 3; 2 by; by three; two by; 2 buy 3; two buy three;buy 3; 2 buy; buy three; two buy

14 times 2 by 3

The answer is 14 times 3 by 2 ;; The area painted is the effect. ;; The volume of paint is the cause. ;; The cause-effect is relation defined by a function involving multiplication by a constant. area equals volume in to 3 by 2 .

Everyday, a hotel sends a worker to buy eggs from market. The eggs are priced at 1 coin each and the worker charges 5 coins for the travel to buy eggs. How many coins are to be given to buy 120 eggs?

120

120 coins

125

125 coins

The answer is "125 coins". ;; The coins is the effect. ;; The number of eggs is the cause. ;; The cause-effect relation is defined by a function involving addition of a constant. ; coins ; equals; number of eggs ; in to ; price per egg ; plus; 5

A car is moving in a straight line at constant speed. It is at a distance 10 meter at 20 second and at a distance 20 meter at 25 second. The "effect" distance is given and the "cause" speed is to be computed. What is the speed.

=;equals;minus;meter;second;2nd;-

speed equals 20 meter minus 10 meter by 25 second minus 20 second

cannot;computed;only;distance;given

speed cannot be computed as only the distance traveled is given

The answer is "speed equals 20 meter minus 10 meter by 25 second minus 20 second". ;; The distance traveled is the effect. ;; The speed is cause. ;; The cause-effect relation is defined by a function involving rate of change speed ; equals ; speed two minus speed one ; by ; time two minus time one.

A car is moving in a straight line at constant speed. It has a velocity of 2 meter per second for first 3 seconds and 4 meter per second for the next 1 second. What is the distance traveled in the 4 seconds.

equals; meter;second; into; plus;per

distance equals 2 meter per second into 3 second plus 4 meter per second into 1 second

cannot;computed;speed;only;given

distance cannot be computed as the speed is only given

The answer is "distance equals 2 meter per second into 3 second plus 4 meter per second into 1 second" ;; The distance traveled is the effect. ;; The speed is cause. ;; The cause-effect is relation defined by a function involving aggregate of change. ; distance ; equals ; speed one into time1 ; + ; speed 2 into time2

From the examples, it is understood that, Definition of function as an expression involves ;; addition and subtraction ;; multiplication and division ;; exponents and roots Apart from these arithmetic operations, quantities may be related by rate of change and aggregate of change. These two topics are covered in differential and integral calculus respectively. In this topic "aggregate of change" is explained.