- #1
Mol_Bolom
- 24
- 0
I just want to see if I got this correct. From what all I've read it seems that I have most of it understood, but eh, I don't trust my judgement...
Lets say we have [tex]f(x) = {{3x^3 + 8x^2 + 7x + 12} \over {4x^2 - 12x - 15}}[/tex]
And the derivative...
[tex]
{d \over dx} f(x) = \lim _{h \rightarrow 0} {{f(x+h) - f(x)} \over h} =
{{
{d \over dx} (3x^3 + 8x^2 + 7x + 12)
}
\over
{
{d \over dx} (4x^2 - 12x - 15)
}} = f'(x)
[/tex]
Thus the integral would be...
[tex]
\int {f'(x)} \textbf{ }dx = f(x)
[/tex]
And if the constants are unknown, thus letting a and b represent the constants...
[tex]
\int {f'(x)} \text{ } dx = {{3x^3 + 8x^2 + 7x + a} \over {4x^2 - 12x + b}}
[/tex]
Lets say we have [tex]f(x) = {{3x^3 + 8x^2 + 7x + 12} \over {4x^2 - 12x - 15}}[/tex]
And the derivative...
[tex]
{d \over dx} f(x) = \lim _{h \rightarrow 0} {{f(x+h) - f(x)} \over h} =
{{
{d \over dx} (3x^3 + 8x^2 + 7x + 12)
}
\over
{
{d \over dx} (4x^2 - 12x - 15)
}} = f'(x)
[/tex]
Thus the integral would be...
[tex]
\int {f'(x)} \textbf{ }dx = f(x)
[/tex]
And if the constants are unknown, thus letting a and b represent the constants...
[tex]
\int {f'(x)} \text{ } dx = {{3x^3 + 8x^2 + 7x + a} \over {4x^2 - 12x + b}}
[/tex]