Integration Q Homework: Integrate 4 with No Respective Variable?

[studentxlol]

Homework Statement

If ∫4x dx is read as integrate 4 with respect to x, then what is there's no x so that ∫4 d?. Integrate 4 with respect to nothing?

 

[Underhill]

studentxlol,

∫4x dx is read, "the integral of 4x with respect to x."

Underhill

 

[HallsofIvy]

Homework Statement

If ∫4x dx is read as integrate 4 with respect to x,

No, it isn't. It would be read as "integrate 4x with respect to x"

then what is there's no x so that ∫4 d?. Integrate 4 with respect to nothing?

$\int 4 d$ is an incorrect notation. You do not need an x in the function to be integrated (it can be a constant function) but you cannot have "d" in an integral without a variable: $\int 4dx= 4x+ C$, $\int 4 dt= 4t+ C$, etc.