The Mathematical Ninja pointed out of the window. "I CAN SEE MY CAR MAKING SMOKE!", he yelled.

The student looked out of the window, said "Oh no!" and then, after a pause. "Hang on, you don't have a car."

The Mathematical Ninja smiled. "Correct. But you'll now remember how to integrate trig functions:

- I - when you're integrating
- can - starts with C, meaning $\cos$, which integrates to...
- see - starts with S, meaning $\sin$, which integrates to...
- my car - starts with MC, meaning $-\cos$, which integrates to...
- making smoke - starts with MS, meaning $-\sin$.

"And $-\sin$ integrates back to $\cos$?" asked the student.

"Correct. Also, when you're integrating, you tend to divide - which means $\int \sin(2x) dx$ would be...?"

"Uh... $-\frac{1}{2} \cos(2x)$?" said the student. "Plus a constant!" he added, hurriedly, catching the Mathematical Ninja's raised eyebrow.

## Colin

Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008.
He lives with an espresso pot and nothing to prove.

## MathbloggingAll

How the Mathematical Ninja integrates http://t.co/8XouQTF5Ic

## Joshua Zucker

This seems really unlike the Ninja’s usual style: he usually does something that reveals some connections or understanding, rather than a mindless mnemonic. Isn’t there a better way he could do this, maybe by thinking about the graphs or the Taylor series or …?

## Colin

That’s true! It’s possible he was in a hurry… or perhaps the Mathematical Pirate has infiltrated… I’ll investigate.