Solve Log Problem: Integral of (1/x) from -b to -a with Formula ln(x)

[yungman]

$$\int_{-b}^{-a} \frac{dx}{x} = ln(x)|_{-b}^{-a}$$

What is this equal to? I don't know how to proceed. Please help.

Thank

Alan

 

[Mark44]

The right side evaluates to ln(-a) - ln(-b) = ln(-a/-b)

In order for ln(-a) and ln(-b) to be defined, both a and b have to be > 0.

 

[gb7nash]

How would you normally solve a definite integral? What does the fundamental theorem of calculus say?

 

[Char. Limit]

Actually, the integral of 1/x isn't ln(x), but ln|x|. That makes everything possible.

 

[Mark44]

Actually, the integral of 1/x isn't ln(x), but ln|x|. That makes everything possible.

Good point...

 

[yungman]

So $$\int_{-b}^{-a}\frac {dx}{x} = ln|x|_{-b}^{-a}= ln\left (\frac a b\right )$$

Thanks