Integration (1 Viewer)

[rawker]

∫13 to 9 dx/(x-7)

How do I intergrate that?

 

[insert-username]

To cut a long story short, you can't integrate it without having done the exponentials and logarithms chapter. You cannot integrate anything to the power of -1 (as this function is) through the normal way. The result is:

[log_e (x - 7)]¹³₉ (since the derivative of the log_e f(x) is f'(x)/f(x))

= ln 6 - ln 2

= ln (6/2)

= ln 3


I_F

 

[sando]

mmm... i hav finishished learning integration but i still havent learnt log

 

[SoulSearcher]

You learn that kind of integration in the log and exponential functions chapter

 

[Mountain.Dew]

in general, when doing calculus for logs:

d (ln[f(x)]) / dx = f'(x) / f(x)

therefore, in reverse:

∫ f'(x) / f(x) dx = ln[f(x)]

mind you, this only applies to log of base e, no other bases. lnx= log_ex