Simplify $$d/dx\int^{x^3}_{t^2}\frac{dt}{\sqrt{x^2+t^4}}$$

I am not getting the it by applyig Leibnitz rule as I am not using it properly

Please someone help

@Mann

@AjayMishra lets continue here

The general formula is $$ \cfrac{d}{dx} \int_{\phi(x)}^{\psi (x) } f(x,t) dt = \cfrac{d \psi(x)}{dx} f(x,\psi(x)) - \cfrac{d \phi(x)}{dx} f(x,\phi(x)) + \int^{\psi(x)}_{\phi(x)} \cfrac{\partial f(x,t)}{\partial x} dt $$

@Jasmine there must be $x^3$ as the upper bound of the integral in your answer.

For more: en.wikipedia.org/wiki/Leibniz_integral_rule

You got that?

@AjayMishra I didnt knew this

Thank you !

Can you do this now?

@AjayMishra yes !

There should $dt$ though in your answer. I bet the author must be Indian.

@AjayMishra no wait

@AjayMishra @AdvilSell

Cone to the above room

What you specifically wanna point out there?

@AjayMishra I was already into discussion on this

$t$ is not constant, it is just independent of $x$, $ \cfrac{\partial y}{ \partial x} = 0$ if $y \ne f(x) $

@AjayMishra I get this you are correct I guuess its a JEE problem I guess there is misprint only

@Mann hi :-)

When is real analysis taught ?

Is it in 1st Semester ?

Which book is good for a novice or a beginner ?

Real analysis is taught in 6th semester

Or 5th

And only to M & C people

You can use book named real analysis by Stephen Abbot 2e

That's the best undergraduate book I think

@Mann okay , thanks !

What topics are taught in 1st Semester ?

@Mann

Pretty easy one in my institute at least

I'd recommend buy one of those "engineering mathematics" book, perhaps by Erwin Kreyszig

It will have all the content you need

It's like a compilation of most important topics, specifically covered in 1st or 2nd year

@AdvilSell

If you wanna study rigourous mathematics. Then I'd suggest do not follow engineering mathematics book. Instead follow some theoretical one, but it will take longer time.

You can still use the real analysis book. It's undergraduate and doesn't require prerequisite. But it will be slightly hard to read at this level. But if you get used to reading such statements at this point of time. You will be able to do really well

Even the basic chapters would do, as long as you practice 'reading' mathematics

Fun question :

Suppose you have the numbers k, k+1 , k + 2 , ... , k+n-1

And let's make a number X by adding all these numbers in all possible combination (with repetition)

Only addition operator is allowed (no subtract)

What are the numbers that can't be covered by X

one of them must be k-1

k > 0 and (n-1>0)

(0,k)

And everything is Integers*

Or just, all non negative integers

okay. No problem. Well, how good is guess (- infinity,2k) ?

@AjayMishra yes this is true. All numbers less than k will not be covered

It will not always hold

But it's going closer yes

Numbers less than 2k are not also covered. you can't add k + 0

If (n-1) > k it will

Anyway I won't spoil it now for a while. I will come back in a bit

Run a for loop from i = 2 to alpha

Fill all the numbers between (i-1) * (k+n-1) to i * k

All these numbers are not possible to cover