Talk:Integral of secant cubed

My two cents
Personally, I feel like nominating this article for deletion on the basis of WP:NOT. However, based on the real life experiences not much different from Silly Rabbit's, I would simaltaneously nominate the following question for the most common question in a Calculus course, by far:


 * Is [the integral of] secant cubed going to be on the test?

This is quite possibly the single most confounding topic in the watered-down version of Calculus (yes, no hyperbolic functions!) taught nowadays. Arcfrk (talk) 10:15, 13 July 2008 (UTC)

I whole heartedly disagree. By reffering to the smae statement you alluded to, "The purpose of Wikipedia is to present facts." A proof, whether mathematical, scientific, etc. Is simply showing how somethign was determined as being fact! —Preceding unsigned comment added by 198.188.6.56 (talk) 18:53, 9 June 2009 (UTC)

Watering down
To say that the problem of watering-down misses the essential thing. Once upon a time calculus was taught to those who wanted to learn mathematics. Now it's taught mostly to those who intend not to learn mathematics and intend to remain outsiders to the subject but want to get some sense of what it is. The sort of people who not only can't solve any math problems except those they've been told how to solve, but who think that's normal; they think it's unfair to include on a test a problem of a sort they haven't been taught how to solve, even if all the material they need to solve it has been taught. Sort of like thinking that when you learn a foreign language you should learn to utter only those sentences you've been taught. So instead of teaching a course suitable for students of that kind, they instead teach a watered-down course. Instead of bemoaning the fact that the students aren't mathematicians and can't handle the traditional sort of course, one ought to design a course suitable for that alien sort of student. Some idiotic attempts in that direction consist of trying to show problems to which calculus is applicable and that such alien students would care about. Some whole textbooks attempting to do that have been adopted in some cases. For the most part they're dishonest and stupid. The remedy is not to write a better version of that sort of book; that's hopeless. Michael Hardy (talk) 15:49, 14 July 2008 (UTC)


 * The diagnosis is spot on, although you may be too harsh on the teachers: after all, it is the pressure from above, beyond even the department level, that creates the phenomenon of disinterested students with "cookbook" attitude taking courses like Calculus; what is the instructor to do then, teach "Math for poets" in its place? What's troubling is that even if you do tell the students: "Yes, the integral of the secant cubed is going to be on the test, you are expected to know how it's derived" (pun not intended), the results are still abysmal: this is what I meant by "confounding topic". Arcfrk (talk) 05:26, 15 July 2008 (UTC)

No, the solution is not "calculus for poets". I guess I was mistaken in thinking it would be apparent what I had in mind as the alternative. Maybe I'll have to write that book myself. Michael Hardy (talk) 13:44, 15 July 2008 (UTC)

Education
If wiki is intended to be informative, why not use this thread to be educational? This is an excellent place to teach hyperbolic substitutions and the value of hyperbolic functions. —Preceding unsigned comment added by 150.176.192.118 (talk) 18:44, 4 May 2010 (UTC)

More challenging?
People, you did not see really challenging integrals!--MathFacts (talk) 09:56, 10 August 2009 (UTC)
 * Obviously there are far more challenging integrals than this, but this is among the more challenging among those with elementary antidervatives that are normally taught to freshmen. Michael Hardy (talk) 00:21, 6 October 2010 (UTC)

Section ordering
It makes more sense to place the hyperbolic derivation above the recersive definitions of higher powers to proceed in more abstract but less involved. —Preceding unsigned comment added by 150.176.192.118 (talk) 15:23, 5 May 2010 (UTC)

Adding integral to both sides
Regarding the step: "Next we add $$\scriptstyle{}\int\sec^3 x\,dx$$ to both sides of the equality just derived": I would like to add a note at this point that combining two indefinite integrals that look the same is not generally valid, without accounting for a possible constant difference. (See Mathematical_fallacy for an example that fails.) Any comments before I do so? — Preceding unsigned comment added by Phildonnia (talk • contribs) 01:15, 10 July 2015 (UTC)


 * That section seems to have been renamed 'Analysis'. Moreover, since we are talking about indefinite integrals, we do not have to worry about the boundaries. The constants of integration can be absorbed into the one appearing in the final answer. Nerd271 (talk) 15:33, 7 April 2020 (UTC)

Student-friendliness
I really like how student-friendly this article is. Steps are shown and clearly explained, making this article useful to beginners. People often forget they were themselves beginners once upon a time, and have to be taught these things slowly. As a professor of mine put it, "Analysis should not be used to impressed." Nerd271 (talk) 15:50, 7 April 2020 (UTC)