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Effin' integrals.

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DrPizza said:
The integral on the left is very similar to an arc length problem (of a parabola) that I assign to my calc I students every year. It's one of my favorite problems because it starts with knowing the formula for finding the arclength, then they need to make a "tricky" trig substitution (replace x with tan(theta), dx with sec²(theta)). Then, to integrate sec^3, they have to do an integration by parts. During the integration by parts, they have to integrate secant, which involves picking "multiply by sec(theta)+tan(theta) over sec(theta)+tan(theta)" out of thin air. (Plus there are some coefficients/constants in there, since it's not simply the length of y=.5x^2 from 0 to 1.)

When I teach them how to integrate sec(x), they always ask "how did you figure out to multiply by that??"

Back when we used chalkboards, it was the best problem in the world to do before an Algebra class - I'd make the solution wrap around the room & would leave it up. "What's all that stuff?" "Oh, that's the answer to ONE of their homework problems last night. Now, you were whining again about how much work the quadratic formula is??"
Click to expand...

just to be cruel, you should use a problem from functional/variational calculus. that shit was crazy! 😉
 
Now your turn to answer our questions, TridenT.

Begin with a generic quadratic equation in standard form: ax^2+bx+c=0. Derive the quadratic formula. Go.
 
MovingTarget said:
Now your turn to answer our questions, TridenT.

Begin with a generic quadratic equation in standard form: ax^2+bx+c=0. Derive the quadratic formula. Go.
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He's taking calc II. If he can't do the above problem, it's pretty sad.
 
DrPizza said:
He's taking calc II. If he can't do the above problem, it's pretty sad.
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I know it has been a while for him. This is why I am curious as to if he can do it. Even if he doesn't remember how, which is fine, it is more an exercise in persistence. Considering TridenT's posts in this thread, this is what I suspect he lacks, which is why I ask him to do this.
 
MovingTarget said:
I know it has been a while for him. This is why I am curious as to if he can do it. Even if he doesn't remember how, which is fine, it is more an exercise in persistence. Considering TridenT's posts in this thread, this is what I suspect he lacks, which is why I ask him to do this.
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I already looked it up online. I definitely wouldn't have given it enough time to know to move the c to the other side, divide by a, etc.

I have other shit to do today, like physics homework. (And a lot of it) And I don't have very much time considering I just woke up because I've been exhausted these past few days.
 
TridenT said:
I already looked it up online. I definitely wouldn't have given it enough time to know to move the c to the other side, divide by a, etc.

I have other shit to do today, like physics homework. (And a lot of it) And I don't have very much time considering I just woke up because I've been exhausted these past few days.
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1) Get more sleep. This has been my own Achilles heel in college and beyond. You cannot function properly without a full night's rest.
2) It is called Completing the Square, and it is very useful. Somehow I graduated high school without knowing how to do it, so I had to relearn. 😵 Go figure. If you don't know how to factor and find roots with this method, spend some time reviewing it.

I wish you luck in your future math problems.
 
TridenT said:
I already looked it up online. I definitely wouldn't have given it enough time to know to move the c to the other side, divide by a, etc.

I have other shit to do today, like physics homework. (And a lot of it) And I don't have very much time considering I just woke up because I've been exhausted these past few days.
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You don't know how to complete the square? Whoa. You're screwed in Calc II when one of the techniques for integration is completing the square.
 
Alright... so, I went to the tutoring center. Guy helped me out. Also had the solutions manual for the book. Basically my whole class has gone to the tutoring center because the guy can't teach for shit. The tutors there are definitely not that good either. They're more of the type that will solve it out and show it to you, which is OK but I'd like it explained at least.

Anyway, the only problem that wasn't solved because they couldn't figure it out (the guy who is the math major) was the 2nd problem on the last image (the white one).

http://img191.imageshack.us/img191/984/14660777.jpg

I felt like I had a moment of brilliance but since I am not very good with the notation and shit I was like, "Damn." and then lost it.
 
TridenT said:
Alright... so, I went to the tutoring center. Guy helped me out. Also had the solutions manual for the book. Basically my whole class has gone to the tutoring center because the guy can't teach for shit. The tutors there are definitely not that good either. They're more of the type that will solve it out and show it to you, which is OK but I'd like it explained at least.

Anyway, the only problem that wasn't solved because they couldn't figure it out (the guy who is the math major) was the 2nd problem on the last image (the white one).

http://img191.imageshack.us/img191/984/14660777.jpg

I felt like I had a moment of brilliance but since I am not very good with the notation and shit I was like, "Damn." and then lost it.
Click to expand...

Of course he doesn't know anything. He's a math major. Math majors spend 2 years with calculus and then move on to pure math.
 
Hacp said:
You're doomed. Someone gave you the answer but you can't resolve the simple steps in between.
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I don't exactly see how I can convert l(x^k) = l(z).

Integrating dz=k*x^(k-1)dx is not really going to get me anywhere. It just proves l(x^k)=l(x^k)... which is useless if I need to prove kl(x) = l(x^k).
 
TridenT said:
I don't exactly see how I can convert l(x^k) = l(z).

Integrating dz=k*x^(k-1)dx is not really going to get me anywhere. It just proves l(x^k)=l(x^k)... which is useless if I need to prove kl(x) = l(x^k).
Click to expand...

Well you have a 3rd equality that you can work with now don't you? Which one is that?
 
Hacp said:
Of course he doesn't know anything. He's a math major. Math majors spend 2 years with calculus and then move on to pure math.
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If you go the "applied" route (i.e. not actuarial math or statistics), it can be three years. Then onto all the theoretical stuff through grad school. Your point still stands though. It is all theorems, proofs, etc. from there. Basic calculus skills tend to get rusty at that point, but not so much that a quick look back in ye olde calculus tome wouldn't fix.

What gets me in TridenT's story is that the TA's would simply work it out for them and basically spoonfed. Too often when I was a TA in a similar situation, this would drive me bonkers. I could give them the answer or work it out for them, but that would do them no good in the long run. They wouldn't learn anything if I did that.
 
god you're such a whiner. when you go to the tutoring center, and they do the problems and show you. you ASK them questions to understand what's going on. take the initiative yourself to learn this stuff and understand it fully, stop fucking making excuses.
 
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