INTEGRATION OR SUMMATION ??????

hey guys !! I was a little bit confused about that what is the difference between integration and summation and how can we convert the summation problems into integration ??

if there is any method, please suggest.

#Calculus

Easy Math Editor

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`2 \times 3`	$2 \times 3$
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Comments

As far as I know...You can't...In reality, Integration is defined as summation over infinite values. For example, if I want you to find the number of students in a class, you will count them and tell me the result.

On the other hand, if I tell you to count number of stars in the sky, then, you would estimate the number of stars in a small area, and integrate all these small areas, which will finally give you the approximate of total number of stars. Hope this helped!

A Former Brilliant Member - 6 years, 5 months ago

but integration can also be done within a limit. as known as definite integration, similarly for summation. does that make any difference??

vipul johri - 6 years, 5 months ago

Yes, see definite integration means that you have fixed an upper and alower limit. But, still there are infinite values in those 2 values. For example, even if you set the values as 1 and 2, but there are infinite numbers betwen these 2 digits.

A Former Brilliant Member - 6 years, 5 months ago

Regular sums are discrete. Integration is continuous.

Mursalin Habib - 6 years, 5 months ago

Can help this : https://brilliant.org/discussions/thread/extremely-weird-integration/?ref_id=946409

柯南 - 5 years, 9 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$