The Math Thread!
- Thread starter Argetlam
- Start date
Sneaky trick, but when obtaining the expression v = x you left out the constant. Should be of the form v = x + a! : )
edit: Actually I guess that explanation isn't really sufficient. Alternatively, you could say that your two integrals in the last line of your derivation are not necessarily equal. log(x) + a and log(x) + b are both valid solutions to Int (1/x) dx even when a=/=b.
@ Posts before: a^(-b) = 1/(a^b)
edit: Actually I guess that explanation isn't really sufficient. Alternatively, you could say that your two integrals in the last line of your derivation are not necessarily equal. log(x) + a and log(x) + b are both valid solutions to Int (1/x) dx even when a=/=b.
@ Posts before: a^(-b) = 1/(a^b)
Could have been worded a bit more formally, but you're correct: indefinite integrals without limits require some sort of constant of integration. And, as you put it, the one on the left could have a different constant (Say, C[sub]1[/sub]) than the right (C[sub]2[/sub]), thus you can't have them cancelled out on both sides of the equation.
Overall, well done. =3
Overall, well done. =3
Haha yeah, sorry for the lazy explanation, you know what I mean though.
An interesting little integral I'll need to end up solving for a project I'm working on,
Int (x^2 + a^2)^(b/2) dx for any integer value of b, where a is some constant.
I don't expect the solution to be nice. People are welcome to take a crack at it, I'll post the method when I work it out!
An interesting little integral I'll need to end up solving for a project I'm working on,
Int (x^2 + a^2)^(b/2) dx for any integer value of b, where a is some constant.
I don't expect the solution to be nice. People are welcome to take a crack at it, I'll post the method when I work it out!
It looks so simple but it's so cruel. I tried out a few ideas, but the derivation is just going to take me too long haha, totally giving in and using Wolfram Alpha (although I would like to learn how it was solved still).
This integration is part of an analytic model I have developed which investigates the distribution of forming stars around a given point. it's a basic model, but I think it's pretty cool, I might post it to show those new to this area of math why integration is such a useful tool.
This integration is part of an analytic model I have developed which investigates the distribution of forming stars around a given point. it's a basic model, but I think it's pretty cool, I might post it to show those new to this area of math why integration is such a useful tool.
I tried Math. THREE TIMES (that's three years worth). I still haven't passed my GCSE. I've given up now as I forget what I've just learnt in math - so I have a Level 2 certificate in math but when tested, I was 2 steps lower, at entry level 3. So I don't think there's any courses I can take anyway. Math will always be something that alludes me I guess. I'll stick with English.
What is the GCSE?
Hipoke, it is highly recommended you take Geometry. You'll want to know about geometry for standardized tests... which are what get you into college. Alg 2 is a little bit of a step up from Alg 1, but not horribly so. You can adjust, you're just going to need to learn quickly. Unless you are mathematically minded, I wouldn't recommend it... but go for it. Which grade are you going into? You'll run out of classes to take in high school if you take Alg 2 in middle school... but it is worth it if you like mathematics competitions.
Well this year I'm in 7th and I'm going into 8th next year. Math has always been a strongpoint for me, the only problem was last year I was in the gifted class but they didn't have Pre Alg as a choice, only the standard 6th grade math, so all "gifted" was, was a bunch of smart kids in a normal leveled class. I moved to Pennsylvania, and I took a test, and since I didn't know much about Algebra (I could do basics like 8 times x equals what but that was basically it) they said I should take pre-alg which I agree with as well, but I believe with some determination I think I can skip algebra one, I was just wondering if it was a good choice in the long run or not.
^As long as you are getting Geometry in your education, you should be fine. While it isn't fun, Geometry is very important moving forward... you definitely won't cover much of it in Alg 2, but it is still important. If that is offered, take it. If not, just advance as you see fit. What you might want to do is talk to the Alg 1 teacher and see if you can pass a comprehensive test. Alg 2 assumes that you know quite a bit about Alg 1 without difficulty. You won't be given much time to completely catch up... but you should be able to learn quickly if you are good at math. If you take Alg 1 in 8th grade, you're still at about the pace you should be at.
Basically, I would put it contingent on whether or not you want to do math competitions. Knowing alg 2 as a freshman gives you a huge advantage in those competitions, but if you aren't planning on doing them, there aren't too many reasons to take alg 2 in 8th grade...
Basically, I would put it contingent on whether or not you want to do math competitions. Knowing alg 2 as a freshman gives you a huge advantage in those competitions, but if you aren't planning on doing them, there aren't too many reasons to take alg 2 in 8th grade...
