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[eerr]

So, I was in calc 2 class recently, near the end of class. The teacher wrote the page #'s on the board for the homework. She then listed not 30, not 20, not 12, but 6 problems.

In previous math classes I always thought: "awesome, less work to do"
When the teacher assinged less problems.

Now, with my elite 'work measurement' knowledge, knowing calculus is Always hard work, I spoke:

"FUCK, theres only 6 problems!"

Tell me about when you expected something, but realized it just aint true!

If your curious, the problems were trig-substitutions, like the indefinate integral of
(Tan x)³ Sec x.

[zchris13]

I'm in AP Calc BC! It's super fun!

Exactly the same thing happens to me!

[qwertyuiopas]

What level of education? I would be so annoyed if I missed something because the rest of my class last year couldn't go through it all as fast as the teacher wanted...

[eerr]

Well worry not, you'll get Moar in college!
: P

What level of education? I would be so annoyed if I missed something because the rest of my class last year couldn't go through it all as fast as the teacher wanted...

Usually its not what the teacher wants, but whatever the board of education "declares".
AP implies college credit, because you can't get credit any higher.

You just stay longer and take classes progressively rated harder if you seek a higher college degree.
The only place you might go is a better college for harder classes.

[qwertyuiopas]

Well, I only got to see derivatives in grade 12 calculus with a mention that if there was more time left over we might have leaned to integrate. On the other hand, that particular teacher gave an open textbook true or false test as half of the final task worth 10-20% of the final grade! (And I don't think anybody got everything right, just showing that it was testing comprehension, not memorization)

[eerr]

unfortunately, L'ohpitals rule, the fundamental theorem of calculus:

F'(x) =(F(x)-F(x+h))/2h

does NOT lend itself to go backwards.

so Integration is based on reversing all the forumulas used for derivatives.
And making lots of substitutions.

In the case just of powers of x
x, x²,x³,x⁴ this is already confusing, you have to increase the power by one and then divide by the power.

If you ever got to LN(x), x^-1, e^x you need a whole new set of rules. And thats before you integrate complex stuff like (x+2)^-1 or e^2x

For these, you need Calc 2 techniques like U substitution, Power rule, quotient rule, Integration by parts.

And all of that is without cracking open trig functions. Trig substitutions alone have a page to themself.

[zchris13]

unfortunately, L'ohpitals rule, the fundamental theorem of calculus:

F'(x) =(F(x)-F(x+h))/2h

does NOT lend itself to go backwards.

so Integration is based on reversing all the forumulas used for derivatives.
And making lots of substitutions.

In the case just of powers of x
x, x²,x³,x⁴ this is already confusing, you have to increase the power by one and then divide by the power.

If you ever got to LN(x), x^-1, e^x you need a whole new set of rules. And thats before you integrate complex stuff like (x+2)^-1 or e^2x

For these, you need Calc 2 techniques like U substitution, Power rule, quotient rule, Integration by parts.

And all of that is without cracking open trig functions. Trig substitutions alone have a page to themself.

12 year calc and we are doing the power rule, quotient rule, and chain rule. They're really fun. Only for the derivitive part so far, so I don't know what may be coming. 2 classes of calc in 1 class. FUN!

[eerr]

unfortunately, L'ohpitals rule, the fundamental theorem of calculus:

F'(x) =(F(x)-F(x+h))/2h

does NOT lend itself to go backwards.

so Integration is based on reversing all the forumulas used for derivatives.
And making lots of substitutions.

In the case just of powers of x
x, x²,x³,x⁴ this is already confusing, you have to increase the power by one and then divide by the power.

If you ever got to LN(x), x^-1, e^x you need a whole new set of rules. And thats before you integrate complex stuff like (x+2)^-1 or e^2x

For these, you need Calc 2 techniques like U substitution, Power rule, quotient rule, Integration by parts.

And all of that is without cracking open trig functions. Trig substitutions alone have a page to themself.

12 year calc and we are doing the power rule, quotient rule, and chain rule. They're really fun. Only for the derivitive part so far, so I don't know what may be coming. 2 classes of calc in 1 class. FUN!

Ahh, thats right.

The easy days, some of those those were derivative rules, it's all coming back to me.

btw, Integration by parts isn't the counterpart to chain rule, its actually the integral of product rule.

so if you hoped any of that stuff was reversible or easy in Integration, prepare to be suprised!

btw, the result of an antiderivative is an integral, I 'think'
either way, the diffrence seems like splitting hairs and won't come up when you actually need to do the math.

[qwertyuiopas]

Derivative vs integration ones?

Also, out of a mild intrest a few days/weeks ago, I checked wikipedia. Their formula images makes simple math look hard, not to mention proofs and university level equations.

[Mephisto]

The memories... I always thought I was good at math, but college killed it for me. Luckily, I'm done with math.

I took Calc 2 or 3 last semester and we covered all that crap. Damned if I can remember any of it, though.

[eerr]

Derivative vs integration ones?

Also, out of a mild intrest a few days/weeks ago, I checked wikipedia. Their formula images makes simple math look hard, not to mention proofs and university level equations.

Honestly the hard part isn't all the fancy terms.

Its the amount of raw math on top of using the fancy terms!

And I don't usually sort rules as  being either for integration or deriving, I just remember what looks like it fits. If I check in my head and it doesn't fit, I expand the range I search for equations, with what I recently learned popping up first.

btw, Integration is much harder than derivatives.
sometimes you need to split an integral into multiple integrals using formulas, or take the derivative to solve a small integration problem.

come to think of it, trig substitution might have been like
x= asin@
with x^2 and a^2 together under a square root.

[Lord Dakoth]

Ha. I took Calc 2 in junior year. Of high school.

Not that I remember much of it, one measly year later.