Tricks and concepts

The objective of this note is to know and tell about the concepts, techniques or tricks which may be helpful during our Jee-prepration and are rather not that popular ( i.e you do not learn them commonly in school or maybe not at coaching too .) so, it will just take few seconds to write down (Our target would be to give at least a concept daily ) but it will help us all ! you may also write something important ( only related to study ) so that you may see it later , It would be great if you all make this note an important one such that we will see it a day or two before jee advanced ! Rules : if you are contributing something , write it's number after 2 hashtags and comment and if you are just commenting , write normally ! ##Enjoy !

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

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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}`	$\boxed{123}$

Comments

5 Whobbling coin : concept is very important, you can learn it here : coin or here .....there are some nice question on brillant related to it too .............. 1 or 2 { although , i solved both of them without learning the concept :P }

A Former Brilliant Member - 4 years, 6 months ago

It is not in the syllabus I guess?

Harsh Shrivastava - 4 years, 6 months ago

yes , but in jee-advanced question can be asked as we saw in jee adv. -2016 that they are shifting their focus from normal to some good level physics ! :)

A Former Brilliant Member - 4 years, 6 months ago

3 Descartes rule of signs : Again , not that uncommon but useful "trick for finding the roots of a quadratic ! You can learn it here or here

A Former Brilliant Member - 4 years, 6 months ago

4 Using Feynman's method of integration can be useful in scenarios where there is a natural logarithm on the numerator of the integrand.

Harsh Shrivastava - 4 years, 6 months ago

method of this trick is to differentiate the integral w.r.t to a constant and then integrate normally !!

A Former Brilliant Member - 4 years, 5 months ago

Yeah.

For example,consider this :

$\displaystyle \int_{0}^{1}\dfrac{1-x^{2016}}{\ln x} dx$

It can be easily solved by using feynman's method!

Harsh Shrivastava - 4 years, 5 months ago

@Harsh Shrivastava – care to show , how ?

A Former Brilliant Member - 4 years, 5 months ago

@A Former Brilliant Member – $F(a) = \displaystyle \int_{0}^{1} \dfrac{1-x^{a}}{\ln x}dx$

$\implies F'(a) = \displaystyle \int_{0}^{1} \dfrac{-x^{a} \ln x}{\ln x}dx = \displaystyle \int_{0}^{1} -x^{a}dx$

Now rest is easy i guess.

Harsh Shrivastava - 4 years, 5 months ago

@Harsh Shrivastava – but bro @Harsh Shrivastava both of them yield different result ! :O , first will give -log(2017) while second one 1/2017 , there is difference of that log !

A Former Brilliant Member - 4 years, 5 months ago

@A Former Brilliant Member – your concept is wrong bro !

A Former Brilliant Member - 4 years, 5 months ago

https://brilliant.org/problems/a-simple-integral-3/

This problem's solution contains some awesome results that are hell useful.

Harsh Shrivastava - 4 years, 6 months ago

solved it, was nice !

A Former Brilliant Member - 4 years, 6 months ago

1 I will begin by giving information about a method called method of images(not that rare but helpful sometimes !) for hindi speaker this will be the best explanation or maybe this : wiki there is a nice question on brilliant too on it here , it deals with the quantitative analysis of charge induced on an equipotential surface !

A Former Brilliant Member - 4 years, 6 months ago

Images are useful in many problems in I E Irodov's book

Kishore S. Shenoy - 4 years, 6 months ago

yeah ! that's why i told it and also wrote (not so rare , if you have some concept to share , do write it ! )

A Former Brilliant Member - 4 years, 6 months ago

@A Former Brilliant Member – I have a method which will solve Irodov's Mechanics Q1.82 in 3 steps. How did you do it?

Kishore S. Shenoy - 4 years, 6 months ago

@Kishore S. Shenoy – drew fbd's and constraint of string length i did in 3-4 steps too ! which method do you wanna propose bro @Kishore S Shenoy ?

A Former Brilliant Member - 4 years, 6 months ago

@A Former Brilliant Member – Balanced horizontal forces and acceleration along the wedge to get acceleration.

Kishore S. Shenoy - 4 years, 6 months ago

2 Abel's theorm for power series : you can learn it here Abel it is useful for calculation of some power series expansion ! you can see other theorms given by Niels Henrik Abel in the related links on wikipedia !

A Former Brilliant Member - 4 years, 6 months ago

6 common sense :P

A Former Brilliant Member - 4 years, 6 months ago

I have posted our challenge problem,do try it!

Harsh Shrivastava - 4 years, 6 months ago

7 i am tired of writing "not that uncommon" but here are cauchy-swartz and generalized mean theorm

A Former Brilliant Member - 4 years, 6 months ago

Cauchy schwarz is really really awesome and useful for manyy problems!

Harsh Shrivastava - 4 years, 5 months ago

9 Some expansions and special series and suggest you remember them too ! :) taylor and basel problem types

A Former Brilliant Member - 4 years, 5 months ago

what do you say : @Prakhar Bindal @Kishore S Shenoy @Avi Ghanshani @Aniket Sanghi @Rajbir Malik @saharsh rathi @Rajdeep Dhingra @neelesh vij @aryan goyat @Rudraksh Sisodia @Swagat Panda help by contributing in any subject ( PCM ) thnx !

A Former Brilliant Member - 4 years, 6 months ago

thanks for mentioning me , bro this sounds cool .. i have some stuff related to the electrical ckts , capacitors and lemme find out more ..

Rudraksh Sisodia - 4 years, 6 months ago

aren't you gonna post ?

A Former Brilliant Member - 4 years, 5 months ago

8 From me too bro : link

hiroto kun - 4 years, 5 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}`	$\boxed{123}$