Can someone tell me why this integral is invalid?

1. Nov 16, 2012

PhiPhenomenon

Hey guys,

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

∫ v Δp = pv + C

2. Nov 16, 2012

Staff: Mentor

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

This is valid:

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

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

3. Nov 17, 2012

Millennial

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

4. Nov 17, 2012

Staff: Mentor

Which is the same as saying y is a constant.

5. Nov 17, 2012

PhiPhenomenon

Ah I see. Thanks guys.