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QuantumTheory
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Ok.
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
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
Last edited: