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FoolForMath
Group Title
Just another cute integral:
\[\int x^3 \; dx \]
and yes this is indefinite ;)
 2 years ago
 2 years ago
FoolForMath Group Title
Just another cute integral: \[\int x^3 \; dx \] and yes this is indefinite ;)
 2 years ago
 2 years ago

This Question is Closed

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.2
Hmm \[ \int x^2 = \left\{\begin{array}{kcc}\frac{1}{4}\cdot x^4, \quad x>0 \\ 0, \quad x = 0 \\ \frac{1}{4}x^4, \quad x<0 \end{array}\right.\]Maybe?
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.0
I have never seen a indefinite integral represented like this.
 2 years ago

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.2
Me neither but I never had to integrate modulus functions without limits before. It has to be like this, I am quite sure.
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.1
\[\int\limits_{}^{}x^3 dx = \frac{x^3*x}{4}+c\] I hope this is right @FoolForMath and congrats on being a new moderator
 2 years ago

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.2
This can't be right, x stays positive but the x^3 can get negative.
 2 years ago

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.2
I am not sure though. and I can be wrong.
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.1
For negative x , x = x and therfore integral value would be positive. Though I can be wrong @ this
 2 years ago

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.2
For negative x, x^3 * x = (x)^3 ((x)) = x^4
 2 years ago

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.2
What's wrong piece wise representation?
 2 years ago

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.2
wait... my piece wise is gonna give same result as yours
 2 years ago

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.2
so, either we are both wrong or right
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.1
\[\huge \int\limits\limits_{}^{}x^3 dx = {sgn(x)}* \frac{x^4}{4}+c\]
 2 years ago

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.2
and your integral does seems better
 2 years ago

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.2
sgn(x) how could i not think about it!?!?! :(
 2 years ago

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.2
so, there are multiple ways of representing same integral?
 2 years ago

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.2
because every integral on this page is gonna get you the same result
 2 years ago

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.2
so, how do you rule out others? and make one right.
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.1
@Ishaan94 , Is my integral right because substitute x and check please
 2 years ago

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.2
x^4/4 is what we will get. sgn(x)x^4/4 = 1* x^4/4
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.1
Yes and why is it negative??
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.1
I have confused myself lolol
 2 years ago

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.2
i am confused myself and blabbering :/
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.1
Same here LOL. However I wolframed it and it is giving my equation. The sgn(x) one. Ditto . ??
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.1
Ok I got it. Taking example always helps
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.1
In that case how is my first equation wrong , the very first one I mentioned ??
 2 years ago

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.2
\[\int_{1}^1 x^3 = \int_{1}^0 x^3 + \int_{0}^1 x^3 = (1/4) + \frac14 = \frac12 \] \[\left[sgn(x) \cdot \frac{x^4}{4}\right]_{1}^1 = \frac{1}4 + \frac14\]
 2 years ago

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.2
Your first integral was right as well
 2 years ago

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.2
My piece wise representation is pelletty :/
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.1
Haha. Maths always confuses us even when we have the right answers . :P
 2 years ago

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.2
yeah hahaha i never had to integrate such indefinite integrals before.
 2 years ago

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.2
Why isn't FoolForMath replying?
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.1
Only 2 people know the answer to your question @Ishaan94 , @FoolForMath and god himself :P
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.0
Lol, I had the answer but I only figured it out why is it working. Thanks to M.se again ;)
 2 years ago

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.2
0 fans lol
 2 years ago

Ishaan94 Group TitleBest ResponseYou've already chosen the best response.2
I beat God! by 455 fans
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.1
LOLOL
 2 years ago

FoolForMath Group TitleBest ResponseYou've already chosen the best response.0
So, the answer is \[ \frac 1 4 x^3 \cdot x +C \]
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.1
Does it matter, @FoolForMath the position of modulus on either x^3 or x :P
 2 years ago
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