Math Is Fun Forum

  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2007-06-29 00:31:46

rgssparky
Member
Registered: 2007-06-29
Posts: 1

trigonometric integration

I have completely forgotted how to integrate a trigonometric function with a power. for example: sin(x^3).
i think it requirs breaking into parts, like u = x^3, v = sin(u), or something like that, but my attempts have failed, and its been years since i have done this. Please help.
Regards
Mark

Offline

#2 2007-06-29 02:18:17

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: trigonometric integration

Integrating sin(x^3) is extremely difficult.  It involves complex numbers and the gamma function.  Perhaps you mean sin(x)^3?  This is much easier.

Edited to add: The technique you tried to use, u-substitution, can only be used when the derivative of "u" is also in your function.

sin(x^3)dx

u = x^3
du = 3*x^2dx

As you can see, du is not in the function.  However, if your function was:

(3x^2)*sin(x^3)dx

Integration would be done by:

u = x^3
du = 3x^2dx

(3x^2)*sin(x^3)dx = sin(u)du

Integrating this would give you -cos(u), which would be -cos(x^3)


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Offline

#3 2007-07-11 13:29:21

Krizalid
Member
Registered: 2007-03-09
Posts: 51

Re: trigonometric integration

Now set

and then it's done.

Offline

#4 2007-07-11 13:48:50

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: trigonometric integration

That would be a great solution, if the problem was integrating sin(x)^3.  But it's sin(x^3).


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Offline

#5 2007-07-11 13:57:25

Krizalid
Member
Registered: 2007-03-09
Posts: 51

Re: trigonometric integration

Yeah, that's pretty much hard.

Anyway

Offline

#6 2007-07-11 15:47:24

Identity
Member
Registered: 2007-04-18
Posts: 934

Re: trigonometric integration

Krizalid wrote:

Yeah, that's pretty much hard.

Anyway

Wow r u serious? Those mathematicians have gone bonkers i tell u eek

Offline

#7 2007-07-12 01:35:58

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,905

Re: trigonometric integration

What is this two-variable Gamma?
Is it some extension to the original Euler Gamma?


IPBLE:  Increasing Performance By Lowering Expectations.

Offline

#8 2007-07-12 04:13:56

Krizalid
Member
Registered: 2007-03-09
Posts: 51

Re: trigonometric integration

That's the incomplete Gamma function.

Offline

Board footer

Powered by FluxBB