In this series, I’m compiling some of the quips and one-liners that I’ll use with my students to hopefully make my lessons more memorable for them.

Consider the integral

The standard technique — other than multiplying it out — is using the substitution . With this substitution . Also, corresponds to , while corresponds to . Therefore,

.

My one-liner at this point is telling my students, “At this point, about 10,000 volts of electricity should be going down your spine.” I’ll use this line when a very unexpected result happens — like a “left” endpoint that’s greater than the “right” endpoint. Naturally, for this problem, the next step — though not logically necessary, it’s psychologically reassuring — is to absorb the negative sign by flipping the endpoints:

,

and then the calculation can continue.

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*Posted by John Quintanilla on February 25, 2017*

https://meangreenmath.com/2017/02/25/my-favorite-one-liners-part-25/