Can someone tell me why this integral is invalid?

[PhiPhenomenon]

Hey guys,

Can someone tell me why this integral isn't valid?

∫ v Δp = pv + C

 

[Mark44]

Hey guys,

Can someone tell me why this integral isn't valid?

∫ v Δp = pv + C

You're treating v as if it were a constant.

This is valid:

$$ \int k~dx = kx + C$$

This is not:
$$ \int f(x)~dx = f(x) \cdot x + C$$

 

[Millennial]

Basically, \displaystyle \int y\,dx = yx + C \text{ iff }\frac{dy}{dx} = 0.

 

[Mark44]

Basically, \displaystyle \int y\,dx = yx + C \text{ iff }\frac{dy}{dx} = 0.

Which is the same as saying y is a constant.

 

[PhiPhenomenon]

Ah I see. Thanks guys.