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Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Multiplying dx into integral

I was checking out a book on calculus, and it had an integral in the form

\displaystyle\int \dfrac{\mathrm d x}{x}

, but I thought that the correct notation to use was

\displaystyle\int \dfrac{1}{x}\: \mathrm d x

Is multiplying dx into the fraction allowed, and are there any benefits to writing it in this form?

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Original post by majmuh24

I was checking out a book on calculus, and it had an integral in the form

\displaystyle\int \dfrac{\mathrm d x}{x}

, but I thought that the correct notation to use was

\displaystyle\int \dfrac{1}{x}\: \mathrm d x

Is multiplying dx into the fraction allowed, and are there any benefits to writing it in this form?

Both forms are fine. They are identical. The first is slightly more succinct.

OP

Original post by Mr M

Both forms are fine. They are identical. The first is slightly more succinct.

OK, but doesn't the first form kind of imply that dx is a term that is multiplied into the integral (which I guess it kind of is in a way), when it is actually an operator?

Original post by majmuh24

OK, but doesn't the first form kind of imply that dx is a term that is multiplied into the integral (which I guess it kind of is in a way), when it is actually an operator?

No it doesn't imply that. It's simply a quicker way of writing the integral.

OP

Original post by Liamnut

No it doesn't imply that. It's simply a quicker way of writing the integral.

K.

Pedant.

OP

Original post by Khallil

Pedant.

That shameless thread bumping :colone:

:colone:

You're one to talk! :tongue:

:tongue:

Original post by Arithmeticae

That shameless thread bumping :colone:

:colone:

You're one to talk! :tongue:

:tongue:

Hahahaha!

:colone:

The pot and kettle come to mind!

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