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Im' confused between the difference of definite and indefinite integrals.

[tex]\int\limits_a_b[/tex]

[tex]\int[/tex]

The first integral here which is [tex]\int\limits_a_b[/tex] is about area below a curve.

Where a and b is the difference of the area under the function f(x). The [tex]\int\[/tex] is just the whole of all of the f(x) dx on an area.

Consider we have an area under the curve.

We will call the function f(x) = [tex]x^2[/tex]

The area under the curve is then defined as:

[tex]\int\limits_a_b f(x) dx = dL[/tex]

The [tex]\int\limits_a_b[/tex] is defined as all of dx of the function f(x) from a to b.

dx is a small infinitely small piece of the area under the curve.

dL is defined as the area.

I do not understand the integral:

[tex]\int[/tex] , which has no limits (a to b).

I know that this integral is backwards differenatation and requires a constant (I don't know what "arbitary" means, I think it means "fixed"?)

Such that,

[tex]\int x^2[/tex] = [tex]1/3^2 + C[/tex]

Help please?

Thanks

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# Definite and Indefinite intregrals.

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