- #1

- 3,802

- 94

## Homework Statement

Find

[tex]\int_2^4{log_{10}xdx[/tex]

## Homework Equations

Use the change of base formula

[tex]log_ba=\frac{log_ca}{log_cb}[/tex]

## The Attempt at a Solution

Using the formula:

[tex]\frac{1}{ln10}\int_2^4lnxdx[/tex]

[tex]=\frac{1}{ln10}[\frac{1}{x}]_2^4[/tex]

[tex]=\frac{1}{ln10}(\frac{1}{4}-\frac{1}{2})[/tex]

[tex]=\frac{-1}{4ln10} \approx -0.1086[/tex]

What my problem is, is that the integral is giving a negative value, but the function of [itex]y=log_{10}x[/itex] is positive for [itex]2\leq x\leq 4[/itex].

So is it that I've made a mistake in calculating this integral, or is the negative value I'm getting legitimate? At this point I would need to reconsider when the integral is ever negative.