Communities

Writing
Writing
Codidact Meta
Codidact Meta
The Great Outdoors
The Great Outdoors
Photography & Video
Photography & Video
Scientific Speculation
Scientific Speculation
Cooking
Cooking
Electrical Engineering
Electrical Engineering
Judaism
Judaism
Languages & Linguistics
Languages & Linguistics
Software Development
Software Development
Mathematics
Mathematics
Christianity
Christianity
Code Golf
Code Golf
Music
Music
Physics
Physics
Linux Systems
Linux Systems
Power Users
Power Users
Tabletop RPGs
Tabletop RPGs

Dashboard
Notifications
Mark all as read
Q&A

Is $x=\int \int \ddot{x}\mathrm dx \mathrm dx$?

+0
−0

I know that multivariable calculus used like this

$$\phi = \int \int x \mathrm dx \mathrm dy$$

But, I was thinking to use double integral for single variable (double integral respect to single variable)

$$x=\int \int \ddot{x}\mathrm dx \mathrm dx$$

Is it correct? Or, there's better way to write it?

Why does this post require moderator attention?
You might want to add some details to your flag.
Why should this post be closed?

0 comment threads

1 answer

+3
−0

While you can integrate twice for the same variable, your equation is not right. $\ddot x$ means deriving $x$ twice with respect to time, that is, $$\ddot x = \frac{\mathrm d^2x}{\mathrm dt^2}$$ which is very different from deriving twice with respect to $x$ (indeed, $\mathrm d^2x/dx^2=0$). To counteract time differentiation, you have to employ time integration, that is, $$\int\int \ddot x\,\mathrm dt\,\mathrm dt$$

Also, since you're using indefinite integrals, you have to take into account the constants of integration. That is, $$\int\int\ddot x\,\mathrm dt\,\mathrm dt = \int (\dot x + C_1)\,\mathrm dt = x + C_1 t + C_2$$

Why does this post require moderator attention?
You might want to add some details to your flag.

0 comment threads

Sign up to answer this question »

This community is part of the Codidact network. We have other communities too — take a look!

You can also join us in chat!

Want to advertise this community? Use our templates!

Like what we're doing? Support us! Donate