# Integral Properties

1. Feb 6, 2008

### AquaGlass

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Last edited: Feb 7, 2008
2. Feb 6, 2008

### Big-T

Differentiation and integration are inverse operations.

3. Feb 6, 2008

### sutupidmath

yep, the integral of f'(x)dx is simply f(x).

4. Feb 6, 2008

### AquaGlass

oh ok I see, so then it is just e ^ (tan^-1(x)) ?

5. Feb 6, 2008

### sutupidmath

+C, do not forget the constant, sometimes it can be really painful if you forget to add a constant at the end.

6. Feb 6, 2008

### AquaGlass

Oh ok, also do I evaluate that function over the interval [a,b] then? I forgot to mention it before.

7. Feb 6, 2008

### sutupidmath

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. Feb 7, 2008

### Gib Z

Theres really no such thing as an indefinite integral =] Its just commonly used shorthand notation.

$$\int f(x) dx$$ really means $$\int^x_a f(t) dt$$ where a is some constant.

9. Feb 7, 2008

### HallsofIvy

Staff Emeritus
No, it doesn't. $$\int f(x) dx$$ is any anti-derivative of f- it involves an arbitrary constant. The "a" in $$\int_a^x f(x) dx$$ determines a specific constant.

10. Feb 7, 2008

### sutupidmath

yep, just evaluate it over the interval [0,1]

11. Feb 8, 2008

### Gib Z

$$\int^x_a f(t) dt$$ plus an arbitrary constant then =]