Integration Q Homework: Integrate 4 with No Respective Variable?

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The discussion centers on the proper notation and interpretation of integrals, specifically addressing the integral of a constant. It is established that ∫4x dx is correctly interpreted as "integrate 4x with respect to x." The notation ∫4 d is deemed incorrect because an integral requires a variable to denote the differential. Correct examples include ∫4 dx = 4x + C and ∫4 dt = 4t + C, demonstrating that while constants can be integrated, a variable must accompany the differential.

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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?
 
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studentxlol,

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

Underhill
 
studentxlol said:

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?
[itex]\int 4 d[/itex] 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: [itex]\int 4dx= 4x+ C[/itex], [itex]\int 4 dt= 4t+ C[/itex], etc.
 

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