## Monday, 18 August 2014

### INTEGRATION EXPLAINED INTUTIVELY

Okay...there is a slight mistake. It should be volume of the cylinder and not surface area of the cylinder.

TAKING ANOTHER EXAMPLE.

### GOING FURTHER AND BUILDING A BRICKWALL, BUT THIS TIME WE WILL REQUIRE DOUBLE INTEGRATION. WHY?

SIMILARLY, TRIPLE INTEGRATION CAN BE USED TO BUILD A FORT OR A ROOM WITH THE HELP OF ANOTHER DIMENSION dz.

### MORE IN DETAIL

On the 25 December 1642, Christmas Eve at 12.00pm…….Isaac Newton was born.

Unlike Normal children who are born in 9 months, young Isaac was born in just 6 months (Such children are called as pre-matured children). The doctor told his mother that her child had barely survived.

He added that such children have a stunted physical growth and will have severe problems in learning and writing as they grow up.
It was true initially.

Young Isaac Newton had problems grasping answers in his early school life. However later he was not only to grasp them but form his own generation of Physics and Mathematics that forms the basis of Mathematics and Physics even till today.

Newtonian Physics( Classical Physics) ruled for about more than 250 years until Albert Einstein formed Modern Physics.

However, his contribution towards Mathematics in the form of Integration (Calculus) is an underrated contribution given by him. It simplified a lot of things for mathematicians.

### DID YOU KNOW????

 Legend has it that while Isaac Newton had just written half the book....a dog of his put the book on fire in the chimney. However in just a period of 6-months he re-wrote the whole book!!!!.

Now what is integration after all?
In short Integration is a short-cut to multiplication.
Now multiplication itself being a short-cut to addition, one can say that Integration is a short cut to addition (summation).

In order to understand integration intuitively.....just keep asking that if you keep adding something in a certain direction.....what will you get?

The direction in which you keep adding is given by dx (along the x-axis direction) ,
dy (along the y-axis direction),
dh( along the height),
d0 ( along a curve of angle 0 ).

Between the integration sign and the dx (or dy or dh or d0),....whatever you put is the magnitude of thing ( I visualize it as a block)  you are putting.

So when you do integration of s2dx...."2" is the magnitude.
"dx" means direction x (along x-axis).

Lets say, you kept adding blocks of 2kilos.....5 times. So x=5.
Answer = 2.x...means 2 x 5 =10.
So if you add blocks of 2 kilos each 5 times....answer is 2 x 5 = 10kilos.

If you add blocks of 2 kilos each 19 times....x becomes 19....so anwer = 2x = 2x19=38.

'x'.....defines how many times or to what extent you kept adding.

RELATED IMAGES

 AREAL INTEGRAL LINK HERE

 GRAPHICAL INTERPRETATION OF INTEGRATION

MATH STACK EXCHANGE LINK HERE

 MATHS IS FUN.COM.....LINK HERE ON INTEGRATION.

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#### The book on visualizing maths thus got written as a sprout of inspiration. The blog followed. Both these are dedicated to you and all such similar minds searching for answers.Visualizing Math & Physics is a blog dedicated to you and all such similar minds searching for answers.

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