How the Mathematical Ninja integrates

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.

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3 comments on “How the Mathematical Ninja integrates

  • 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.

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