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Need math guys asap!

TecHNooB

TecHNooB

Diamond Member
So it's senior year and i've been slacking off. That's the excuse i'll be using until I find a better one. So anyways, the finals are coming up and I don't want to do piss poor on them and I need some help on integration. I know basic integration but not all of the techniques you need for solving some of em. I'll post some questions. Type out explanations as best as you can, thnx!

INT = integral..
1. INT (X+5)/(X-2) dx
2. INT X*(Cos^2 (5x)) dx


I'll post more as I run into more trouble problems. THNX ATOT
 
question 1 is an improper fraction. Divide them before you integrate; then the integration should be simple.

question 2: simple common trig substitution (look at your double angle formulas for cos2x) Then integrate.

So, your trouble isn't the calculus step...
 
Originally posted by: EvilYoda
Do what any proper ATOTer in high school would do - buy a TI-89.
Click to expand...

I've got one! ...But I won't feel good unless I'm able to solve integrals by hand.
 
Originally posted by: DrPizza
question 1 is an improper fraction. Divide them before you integrate; then the integration should be simple.

question 2: simple common trig substitution (look at your double angle formulas for cos2x) Then integrate.

So, your trouble isn't the calculus step...
Click to expand...

We'll.. let's say manipulating the questions to a form I can solve..
 
Originally posted by: EvilYoda
Do what any proper ATOTer in high school would do - buy a TI-89.
Click to expand...

Any any proper ATOTer with a prof/teacher who knows better would ban their use in the classroom.

If you pretty much want to cheat your way through math, get a TI-89 if you can get away with it. For what it's worth, I'm familiar with a prof at the University of Buffalo who had a class 2 semesters ago, of which, over half of the kids thought they were going to breeze through it because they took it in high school, but wanted the easy A to help their GPA in college. He said that about 10 of them had apparently learned on a TI-89. They didn't know anything, and once their crutch was removed, all but one of the TI-89 dependent students *failed*. They didn't "know" calculus, they had only learned how to use their calculator. Apparently the problem went back to even before pre-calculus... the kids (many from the same high school) hadn't learned math in years... they just knew which buttons to push.
 
Originally posted by: TecHNooB
Originally posted by: DrPizza
question 1 is an improper fraction. Divide them before you integrate; then the integration should be simple.

question 2: simple common trig substitution (look at your double angle formulas for cos2x) Then integrate.

So, your trouble isn't the calculus step...
Click to expand...

We'll.. let's say manipulating the questions to a form I can solve..
Click to expand...

you're saying that you don't know how to do long division or synthetic division of polynomials??

Certainly, you must have learned how to do partial fraction decomposition... and if you did, you should have been practicing long and/or synthetic division at that time...
(If you're wondering where in your notes to look)

For the 2nd problem,
cos2x = cos^2x - sin^2x
= 2 cos^2x - 1
= 1 - 2sin^2x

One of those three can be rearranged to give you the necessary substitution.
 
Originally posted by: DrPizza
Originally posted by: TecHNooB
Originally posted by: DrPizza
question 1 is an improper fraction. Divide them before you integrate; then the integration should be simple.

question 2: simple common trig substitution (look at your double angle formulas for cos2x) Then integrate.

So, your trouble isn't the calculus step...
Click to expand...

We'll.. let's say manipulating the questions to a form I can solve..
Click to expand...

you're saying that you don't know how to do long division or synthetic division of polynomials??

Certainly, you must have learned how to do partial fraction decomposition... and if you did, you should have been practicing long and/or synthetic division at that time...
(If you're wondering where in your notes to look)

For the 2nd problem,
cos2x = cos^2x - sin^2x
= 2 cos^2x - 1
= 1 - 2sin^2x

One of those three can be rearranged to give you the necessary substitution.
Click to expand...

But it's (Cos 5x)^2..

And it's not the division itself.. it's seeing that dividing has to be done in the first place that's getting me. Right off the bat, I made u = x+5 and dv = 1/(x-2) and that ultimately got me nowhere. Dividing led me to the right answer tho, so all is good =)
 
okay, so write the formula as cos 2theta = 2cos^2 theta - 1
and substitue 5x for theta.
Rearrange, and substitue for the (cos5x)^2
 
Originally posted by: TecHNooB
So it's senior year and i've been slacking off. That's the excuse i'll be using until I find a better one. So anyways, the finals are coming up and I don't want to do piss poor on them and I need some help on integration. I know basic integration but not all of the techniques you need for solving some of em. I'll post some questions. Type out explanations as best as you can, thnx!

INT = integral..
1. INT (X+5)/(X-2) dx
2. INT X*(Cos^2 (5x)) dx


I'll post more as I run into more trouble problems. THNX ATOT
Click to expand...

1) (x+5)/(x-2) = 1+7/(x-2). You should then be able to easily integrate that.

2) cos(5x)^2 = (1+cos(10x))/2. Therefore you need to integrate (x+xcos(10x))/2. Integrate xcos(10x) by parts.
 
Originally posted by: DrPizza
Originally posted by: EvilYoda
Do what any proper ATOTer in high school would do - buy a TI-89.
Click to expand...

Any any proper ATOTer with a prof/teacher who knows better would ban their use in the classroom.

If you pretty much want to cheat your way through math, get a TI-89 if you can get away with it. For what it's worth, I'm familiar with a prof at the University of Buffalo who had a class 2 semesters ago, of which, over half of the kids thought they were going to breeze through it because they took it in high school, but wanted the easy A to help their GPA in college. He said that about 10 of them had apparently learned on a TI-89. They didn't know anything, and once their crutch was removed, all but one of the TI-89 dependent students *failed*. They didn't "know" calculus, they had only learned how to use their calculator. Apparently the problem went back to even before pre-calculus... the kids (many from the same high school) hadn't learned math in years... they just knew which buttons to push.
Click to expand...


well in calc classes, wouldnt you only get 1/5 or 1/10 for an answer you have without showing any working? all the calc classes i took were like that
But a TI-89 really does help when you're doing stuff like thermo and you dont feel like integrating etc.
 
Originally posted by: blahter
Originally posted by: DrPizza
Originally posted by: EvilYoda
Do what any proper ATOTer in high school would do - buy a TI-89.
Click to expand...

Any any proper ATOTer with a prof/teacher who knows better would ban their use in the classroom.

If you pretty much want to cheat your way through math, get a TI-89 if you can get away with it. For what it's worth, I'm familiar with a prof at the University of Buffalo who had a class 2 semesters ago, of which, over half of the kids thought they were going to breeze through it because they took it in high school, but wanted the easy A to help their GPA in college. He said that about 10 of them had apparently learned on a TI-89. They didn't know anything, and once their crutch was removed, all but one of the TI-89 dependent students *failed*. They didn't "know" calculus, they had only learned how to use their calculator. Apparently the problem went back to even before pre-calculus... the kids (many from the same high school) hadn't learned math in years... they just knew which buttons to push.
Click to expand...


well in calc classes, wouldnt you only get 1/5 or 1/10 for an answer you have without showing any working? all the calc classes i took were like that
But a TI-89 really does help when you're doing stuff like thermo and you dont feel like integrating etc.
Click to expand...

Just about all of my undergrad math classes and a number of my physics classes did not allow any calculators for their tests. And that's the way it should be as Dr. Pizza has explained. You don't learn anything by using these kind of calculators or math programs to solve the problems for you. And nobody is going to hire you to do the work that a $150 calculator can do either. The amount of insight and knowledge that you acquire by working these things out by yourself can really be amazing. Feynman has a good book of anecdotes and it's really impressive to read about the difference between someone using math and understanding math. And the stuff they had to know to be able to do calculations before electronic calculators is really neat.

Hell, reminds me how students in my class would ask me if the equation for the time constant of a RC circuit is 1/(R*C) or R*C. If they stopped and thought for 10 seconds they would realize what it is. A time constant is on the order of less than one. Common resistor values are 1K and common capacitor values are 10^-6. So which one is more reasonable, 10^-3 seconds or 10^3 seconds? :sigh:
 
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