Simple physics integral help

[wooden dragon]

Can someone tell me where the 1/2 comes from in the right? How did we go from m to m/2? Thanks.

[urban terrace]

you have to do an integration by parts

Integral of v'v = v'^2 - Integral of v'v
=> 2 Integral v'v = v'^2

[frozen rampart]

Azyrashacorki

[spark jungle]

And that $\vec{v}\cdot \vec{v} = v^2$

[frozen rampart]

Azyrashacorki

[grim jacinth]

$\dv{\vec{v}}{t}$

[frozen rampart]

aPlatypus

[grim jacinth]

you have the physics package right?

[spark jungle]

Hum

Idk?

[grim jacinth]

well you used dd, that's a physics package thing

dv is also inside

[gaunt flicker]

Appears so.

[spark jungle]

Ahhh

I didn't know lol

[grim jacinth]

and to cheat a lil bit $\dv{}{t}$

[frozen rampart]

aPlatypus

[spark jungle]

Ooooo fancy

Thanks!

[gaunt flicker]

You can check out the physics package documentation on ctan. Quite handy.

[spark jungle]

I think I just had it because I wanted actual straight dx's for integrals but this all looks so handy

[frozen rampart]

Killuminati

[gaunt flicker]

Not really something you have. It's built into the bot.

[spark jungle]

Yeah prob part of the default preamble on here

[wooden dragon]

hm

i still can't understand

[spark jungle]

The product rule applies to dot products like it applies normally for products of functions in one variable.

[frozen rampart]

Azyrashacorki

Azyrashacorki

Azyrashacorki

[wooden dragon]

Product rule*, right? Thanks for spelling this out for me, very helpful. I understand now.

.solved

[hot forge]

Solved

Post marked as solved by @wooden dragon.

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