Why do I have to learn how to solve integrals by hand when a computer can do it for me...

Why do I have to learn how to solve integrals by hand when a computer can do it for me? Imagine having to compute divisions and multiplications of large numbers with half a dozen decimals. Integrating manually is just as tedious. There's a reason we have computers.

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Because computer can't do it for you (in any nontrivial case) and it teaches discipline, which you millenials and gen z commies lack.
You also learn arithmetic operations to understand them and get familar with them. Now back to doing that highschool homework, little snot.

>implying that the majority nontrival integrals don't end up being evaluated numerically

>Integrating manually is just as tedious. There's a reason we have computers.
Computes are for performing calculations quickly, not a substitute for understanding what you're doing.
Stop being a lazy shit and pay attention to the lecturer.

>divisions and multiplications

bullshit. Haven't you used pretty much any symbolic math solver?
docs.sympy.org/0.7.1/modules/integrals.html

>tfw I'll probably graduate college in a math major doing no integrals and never learning

It just doesn't seem interesting

>implying computers are better than humans at integration

Welcome to the state of math education for everyone until the math major exclusive classes and the reason for a Mathematician's Lament

So why do we teach people to solve problems by hand rather than teaching them to understand calculus?

I don't know about you, but as I recall, most of the homework and lectures focused on implementing new rules, theorems, and other shortcuts to solve integrals (by hand) faster, with relatively little emphasis on what an integral actually is/does and how it is applied outside of an academic setting.

Learning how to solve equations numerical was way more interesting and useful than anything I learned in calculus.

>So why do we teach people to solve problems by hand rather than teaching them to understand calculus?
Because teaching people to solve problems by hand is part of teaching them calculus.

>relatively little emphasis on what an integral actually is
What the hell?

>how it is applied outside of an academic setting.
What do you mean by "outside an academic setting"? You're taking a first-year calculus course. Applications are going to be covered in courses that depend on that knowledge

If you graduate in math, then you'll have to go through analysis, then you're gonna have to learn it all.

>Because teaching people to solve problems by hand is part of teaching them calculus.

It is one way to teach calculus. One way to learn a language is to write down each word and it's definition a hundred times. I'm not sure either is particularly effective.

Now imagine if, in addition to learning a language by writing definitions, they also spent significant portions of the class just teaching you techniques to write definitions faster.

Have I ever used the power rule since I finished calculus? I think I did once, on an exam in a different math class. Could I prove it is a true fact about integrals that the power rule works? Probably, might take a minute. Was there any point in taking 2-3 weeks out of the semester to learn it (and other similar rules)? Not really, it's only use is to solve equations faster, something which you will (almost) never do outside of an academic setting.

>>relatively little emphasis on what an integral actually is
>What the hell?

And when I say relatively little, I mean almost none. As I recall, the course went something like this. The first day of class we come in, talk about what a limit is for thirty minutes or so, and then spend the rest of the next three-four weeks learning how to solve limits by hand, and various theorems that will solve limits by hand. Concluding that, 30 minutes on what a derivative is and how it relates to a limit, 3-4 weeks on learning how to solve derivatives by hand and theorems that will let us solve derivatives faster. And so on for the next three semesters.

Never before have I felt a class was such a waste of my time. Solving problems by hand isn't completely pointless. Maybe spend a week where you have one assignment, in which they solve problems by hand, per topic area. But the entire focus of the course should not be on learning how to solve equations by hand efficiently.

That sounds like a high school or maybe 100 level Calc 1 class, other courses are mostly proving things and it's perfectly acceptable to evaluate an integral with Mathematica and say as much in a problem set.

It was calc one, calc two and three weren't much different. Most of my undergraduate math courses weren't much different. Knowing how to solve an problem by hand always seemed to be the primary goal.

In my graduate courses I do use mathematica to evaluate integrals on my homework, and it's usually fine. Still have to evaluate integrals by hand on the in class exams, because those are still a thing for some reason.

Calculus in particular still really gets my goat for some reason, though. I think it's because the content could easily be condensed into a one semester course, if there wasn't such a fetishization of learning how to do everything by hand because "what if someday you don't have a calculator," or "I had to learn how to do it this way in the sixties, so, so do you."

Haven't you done anything beyond undergrad engineering calc? is an example of what kind of integrals come up all the time in nuclear. Go back to sucking dicks, engineers and let us big boys handle the math.

Because computers are ass bad at it while calculus can get the job done with an exact result.

t. CS major

brap

I don't know how to enter most problems into a calculator, there needs to be one with a camera and you take the picture and it tells you exactly what to write where to make it look like you did it. Math is pointless.

Camera is diffuclt to use. why not alexa and reed numers and lines and dots to machine?

>I don't know how to enter most problems into a calculator
>Math is pointless.

OP kind of has a point. Instead of learning to solve difficult integrals you'd be better off learning to prove theorems of calculus.

You´re either a European studying at a technical college or a liar. Calc 1 in any respectable European university engineering program covers limits, derivatives, integration, transcendental functions, trigonometric functions, power series, applications of integration and applications of derivation in in semester, i.e. 7-8 weeks.

In university, the problem solving is homework, while lectures cover definitions, theorems and brief demonstrations applications.

calc should be taught as:
1.theorems
2. simple example
3. learn how to solve with matlab, other software tools

Nope

What the fuck? Where in the world are engineers not required to take AT LEAST complex analysis?

Why does mommy make me do my chores when I could just watch cartoons all day?