Math Is Fun Forum

GurraTedden

Member

Registered: 2005-07-20

Posts: 19

Integration...

Hi guys, I'm stuck again!
And it's mathematical, like always (regret those lazy days back in analytic math courses, haha).

I'm in this situation:

dx=asin(y)dt

(a is a constant value)

where y=y(t)

I want to solve this for x.
smthing like x = smthing + C (constant of integration, or what ever you want to call it)

I can recall it had something to do about, maybe substitution, but i can't see how thats going to happen...

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 49,693

Re: Integration...

dx=asin(y)dt

(a is a constant value)

where y=y(t)

∫dx = ∫ asinyt dt
∫dx = a ∫sinyt dt

x = a(-cosyt/y) + Constant ???????????

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

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GurraTedden

Member

Registered: 2005-07-20

Posts: 19

Re: Integration...

I'm not convinced... i dont get it really. Do you mead x = a(-cos(yt/y)) ?
How do i differentiate that one and get the same thing in the brickets sin(y).
Ganesh... maybe i didn't make my self clear that y is a function of t.?? Or is it
me that have misunderstood you? Coud you show me how you diferentiate the
expression?

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Integration...

dx=asiny(t)dt
∫dx= ∫asiny(t)dt
x=a ∫sin y(t)dt
Do we know what the function of t is? If so, the rest would be much easier...

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Why did the vector cross the road?
It wanted to be normal.

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Integration...

Forgive me if I am wrong, but it may simply be impossible without knowing the function y(t).

dx = a sin(y(t)) dt

Let us just call the funtion "ƒ" instead of y:

dx = a sin(ƒ(t)) dt

If, for example, there were no sine or factor applied, we could have:

dx = ƒ(t) dt

Which is just a general statement.

So, yes, what is y(t) ?

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

GurraTedden

Member

Registered: 2005-07-20

Posts: 19

Re: Integration...

So, can't we express it in the first derivates of y(t) ? Thats what i'm looking for.
some kind of chainrule or smthing?