# Can someone tell me why this integral is invalid?

Hey guys,

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

∫ v Δp = pv + C

Mark44
Mentor
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:
$$\int f(x)~dx = f(x) \cdot x + C$$

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

Mark44
Mentor
Basically, $\displaystyle \int y\,dx = yx + C \text{ iff }\frac{dy}{dx} = 0$.
Which is the same as saying y is a constant.

Ah I see. Thanks guys.