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Thought-Process to Discover Knowledge

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User Guide

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summary of this topic

### Basics of Integration

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

### Integral Calculus: Understanding Application Scenarios

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

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In this page, the application scenario of integrals is explained with examples.

Keep tapping on the content to continue learning.
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 10cm

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

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 10m at 20sec and at a distance 20m at 25sec. 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

•  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

Progress

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
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?
14 times 3 by 2
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.

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