Integral Properties: Real Estate Solutions

In summary, the conversation discusses differentiation and integration as inverse operations. The integral of f'(x) dx is simply f(x). The integral of e^(tan^-1(x)) is e^(tan^-1(x)) + C, where C is the constant. The function should be evaluated over the interval [a,b], and there is no such thing as an indefinite integral, but it is commonly used as shorthand notation. The notation \int^x_a f(t) dt means finding any anti-derivative of f(x) with the constant a. Lastly, the integral should be evaluated over the interval [0,1] plus an arbitrary constant.
  • #1
AquaGlass
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  • #2
Differentiation and integration are inverse operations.
 
  • #3
yep, the integral of f'(x)dx is simply f(x).
 
  • #4
oh ok I see, so then it is just e ^ (tan^-1(x)) ?
 
  • #5
+C, do not forget the constant, sometimes it can be really painful if you forget to add a constant at the end.
 
  • #6
Oh ok, also do I evaluate that function over the interval [a,b] then? I forgot to mention it before.
 
  • #7
AquaGlass said:
Oh ok, also do I evaluate that function over the interval [a,b] then? I forgot to mention it before.

Are u taking the indefinite or definite integral of that function? Why don't you show the original question first? it usually makes it easier for everyone!
 
  • #8
Theres really no such thing as an indefinite integral =] Its just commonly used shorthand notation.

[tex]\int f(x) dx[/tex] really means [tex]\int^x_a f(t) dt[/tex] where a is some constant.
 
  • #9
Gib Z said:
Theres really no such thing as an indefinite integral =] Its just commonly used shorthand notation.

[tex]\int f(x) dx[/tex] really means [tex]\int^x_a f(t) dt[/tex] where a is some constant.
No, it doesn't. [tex]\int f(x) dx[/tex] is any anti-derivative of f- it involves an arbitrary constant. The "a" in [tex]\int_a^x f(x) dx[/tex] determines a specific constant.
 
  • #10
yep, just evaluate it over the interval [0,1]
 
  • #11
[tex]\int^x_a f(t) dt[/tex] plus an arbitrary constant then =]
 

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