Tag: integration

L’Hopital’s Limit From A Phone Game

One of my recently graduated students was playing a phone riddle game that required an answer to this level: Turns out the solution to the game was just simply the word “answer” as the instruction was to simply enter that in. However, the integral and the limit shown there...
Read More

Special Integral: \(\int_0^\frac{\pi}{2}\ln(\sin x)\;dx\)

I remember when I was in Year 12, we were given this question on an integration worksheet that challenged my friend, Parth, and I so much so that we stayed back after school to use the large whiteboard to solve this problem even after all our friends had left...
Read More

Things to Reconsider: The Integral of \(\frac{1}{x}\)

Absolute Absolutes? Consider the following integral: \[\int \frac{1}{x}\,dx = \log_e|x| + C\] When learning this integral, teachers often stress the need to include the absolute value signs. The reasoning behind this is often to do with the fact that the logarithm of a negative number is undefined. However, is...
Read More