Ceci n'est pas un pipe

23 October 2013

Today in Calculus II:

You’ll notice that there’s three symbols in this term, which makes integration by parts impossible. But there’s not actually three symbols there. No, like Magritte before me, I must tell you that this is not a pipe – or in this case a three-symbol term. It’s actually a very compact little two-symbol term.

Let me remind you of the Double-Angle Formula:

Therefore, we could easily rewrite that to be just as true:

This is easily accomplished using integration by parts, which seems to be my theme for this month.

The remainder of which is easily integrated and simplified.

This is a solution for §7.1 Exercise #21 from Calculus: Early Transcendentals.