i've been doing integrals of trig functions because it's my weakest point.
there are a few basic things that i don't understand.
for eg. i KNOW that:
but please explain this, why is...
1-(Cos^2)2x = 1-Cos4x
(Cos^3)2x = (1-(Sin^2)2x)Cos2x
first of all, i have to inform you that this is not any sort of homeworks. i'm a student and i have an exam at the end of next month. analysis isn't really my teritory, neither is math overall. :)
most of the stuff i put on this paper is...harder for me to solve. some of it are implicit derivative which should be easy but i just need your help to clarify some stuff.
i would really appreciate if you could take some time to help me out, at least with some of the exercises.
i have a problem with integrals of trig functions.
let me explain on an example...
i get to the point where i use the substitution method.... Sinx=t--->cosxdx=dt
when i include this into my function i get this.... ∫ ((1-t^2)/t^1/2)dt...
i don't get the next part of the procedure... ---> ∫(t^-1/2)dt - ∫(t^3/2)dt....
this last part i don't understand...
i don't understand how they get the t^3/2...explanation please
btw i know the stuff such as (cos^2)x=1-(sin^2)x and that so that i understand
i'm not really THAT new on this forum but still haven't introduced myself properly.
so...what the hell am i doing on this forum? (OMG it's a math forum! and WHO(!) likes math?!!)
yea well i really do hate it. but i gotta study some math aswell for my university. btw i study computer science, but they're gonna MURDER me with all this math. it's like i'm studying math and not computer science.
i just had my second math exam for the third frickin time! and almost EVERY TIME they "invent" some field of math that i don't know. btw the exam is about limes functions, integrals, derivatives and financial math. i went through every type of this stuff but like i said, they add some new math.
i'm slowly but surely going nuts because of math. i don't have the will and the power to start learning for my other exams before i finish math. besides, in my case, math probably burns more calories than boxing, so i'm always way too tired to go and grab another book after studying math.
i have to say i'm proud that even i can help out someone:
i got the solution to the 2 task...it actually couldn't be easier.
6/(x-2) - 1/(x+5) = 2/x^2+3x-10
6/(x-2) - 1/(x+5) = 2/(x-2)(x+5) /(x-2)(x+5)
6(x+5) - (x-2) = 2
5x = -30 /:5
x = -6
see?? not so hard...the only thing that you HAVE to notice is x^2+3x-10, which can also be written in form of (x-2)(x+5)
when u multiply the first two variables of each bracket (x,x) you get the X^2, when you sum up the second two variables (-2, 5) you get the 3x, and when u multiply them (-2, 5) you get the -10.
that's the way this thing works. you practice that, you have to be experienced enough to spot this as soon as you look at the exercise.
hope i've been helpful
hey kyle...i got another one for you. i want u to solve this one, because i think that the solution in the book is not correct. the book was written by some of my teachers, they probably wrote the darn book in one night. so many mistakes.
ok here it goes:
∫ 3dx / 4(2-5x)^4/5 =
the solution given in the book goes like this:
I=-3(2-5x)^1/5 / 4 + C
hi everyone, plz don't laugh at me, i'm a math noob, i'm currently learning integrals and i got a problem. i dont understand how to solve this exercise:
∫ 4th sqrt(3x-5)³ dx (it's not 4 x, it's 4th root)
1. now...i usually take this under the brackets and derivate it:
3x - 5=t
the solution should be: I = 4 X 4th sqrt (3x-5)^7 / 21 + C
my math-english is not that good so.. this 4th sqrt should mean fourth square root