Solution to the Do-the-antiderivative-wrong Challenge
Wherein I use the reverse power rule to integrate 1/x. Hilarity ensues.
In the last newsletter, I asked readers to try calculating the antiderivative of 1/x using the reverse power rule. Here’s my solution.
We’ll use this method to find the area under the 1/x curve between 1 and some number b, greater than 1.
There’s the reverse power rule in the second line.
I like this because it’s a general solution to integration of polynomials. Here’s how it works for x².
Integrating 1/x isn’t at odds with the reverse power rule. It’s just that the limit has to be applied more carefully to show that the result is ln x.
In case you missed it, here’s the edition where I issued the challenge.
If you like impossible, try doubling the cube, Euclidean style. This was an open problem for about two thousand years. It was proven an impossible task in the 19th Century. Here’s why:
Until next time, keep playing with maths. You won’t break it.
Adam
PS: If you’re wondering where that last step came from, where I take the limit to get ln b, it’s in a previous post: Fall in love with e all over again.
