# Tag Info

### Explaining difference between improper integrals that converge and diverge

As Sue VanHattum suggests, it makes sense to shift gears to series first, for simplicity. I would also do two examples of series with decreasing terms, one where it's obvious that it converges, and ...
• 41

### Explaining difference between improper integrals that converge and diverge

I'd say: Don't trust your eyes, especially not when infinity is concerned and you are plotting in one small region. Sure, they look fairly similar when you are plotting over $[1,10]$. $1/(1+x)$ in ...
• 4,774
Accepted

### Explaining difference between improper integrals that converge and diverge

Perhaps it's easier for students to see the reason for these results when you are looking at infinite series. Does the course you teach include this? (If not, you can still do it and set up a diagram ...
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### Explaining difference between improper integrals that converge and diverge

To me (a dumb troll), the way to intuitively think about it is 0 versus infinity. Infinity makes things huge. Zero makes them small. So, if you have an asymptotic approach you have a huge (to ...
• 57

### Why is differential calculus often presented before integral calculus?

I have come to realize another very practical reason for teaching differentiation before integration. In most applications of integration we are splitting something (area, volume, arclength, work, etc)...
• 19.5k

### Multivariable Calculus Project Ideas

I have 3d printing as an extra-credit option for some projects, which are usually framed as a (fictional) business person looking for math equations to use specifically so they can then 3d print their ...
• 41

### Unusual applications of integration

One that you see (saw) in chem classes was the "cut and weigh" method of integrating area under the peak for strip chart recorders. https://books.google.com/books?id=igR_jsqfcowC&pg=...
1 vote

### Unusual applications of integration

Something you can do to generate more diverse problems is to combine the problem types from your textbook. You can also be explicit about the kind of work you want them to show you, and make it clear ...
• 19.5k

### How does one tutor an A-level student past the derivative paradox?

I'm not sure how I missed this question when it was first posted, and it already has many answers, but I feel there are some important things that still need to be said to address your specific ...
• 696
Accepted

### Is "Annular Ring" redundant?

I argue that annular ring is not redundant because in common use annulus and ring are not synonyms. Put another way, not all rings are annular. The adjective annular is used to emphasize that the ring ...
• 5,083