Why can we multiply by $dt/dt$ to change variable of integration? Please look at equation 5-20

Question

I am struggling to understand why can we just multiply by $dt/dt$. I was thinking it was just a change of variables, but I cannot come up how that works. Can someone explain why we are allowed to do this?

score 1 · Accepted Answer · answered Dec 01 '20 at 18:24

1

$x=x(t)$ being a function of time, we can compute it's total differential:

$$dx = \frac{dx}{dt}dt$$ and thus,

$$\int f(x)dx = \int f(x(t))\frac{dx}{dt}dt$$

answered Dec 01 '20 at 18:24

fgoudra

972

Why can we multiply by $dt/dt$ to change variable of integration? Please look at equation 5-20

1 Answers1