Food for thought

## Problem

Solve the following integrals:

• $\displaystyle{\int_{2}^{3} \dfrac{1}{x} \, dx}$

• $\displaystyle{\int_{-3}^{-2} \dfrac{1}{x} \, dx}$

Did you make any assumptions, and if so, what were they?

Sketch the following functions along with their gradient functions on the same set of axes.

• $f(x) = \ln (x)$
• $g(x) = \ln (-x)$

What are the domains of $f(x)$ and $g(x)$?

Using your sketch to help you, write down the derivatives of $f(x)$ and $g(x)$.

What do you notice about the derivatives $f'(x)$ and $g'(x)$?