Solve the following integrals:

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

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

What’s the same and what’s different about your solutions?

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 \(g'(x)\)?