# Integration Hell

1. Dec 2, 2003

### BLUE_CHIP

Someone fix my tex pls....

I'm only 16 so i put this on the K-12 forum but they cant seem to help....

OK. I've had a little break from my studdies and need some help with this...

$$I_n(x)=\int\limits_0^x \tan^n{{\theta}}{{d\theta}},n\leq{0},{{x}}<\frac{\pi}{2}[\tex] By writing $$\tan{\theta}[\tex] as [tex]\tan^{n-2}{\theta}\tan^2{\theta}[\tex], or otherwise, show that [tex]I_n(x)=\frac{1}{n-1}\tan^{n-1}{x}-I_{n-2}(x), n\leq{2},x<\frac{\pi}{2}[\tex] Hence evaluate [tex]\int\limits_{0}^{\frac{\pi}{3}}\tan^4{\thet a}d\theta[\tex], leaving your answers in terms of [tex]\pi[\tex] Thanks (Goddam further maths) 2. Dec 2, 2003 ### lethe 3. Dec 2, 2003 ### lethe bulletin board commands like [ /tex ], get slashes. LaTeX commands get backslashes like \Sum OK. here we go: [tex] \begin{gather*} \tan^n \theta=\tan^{n-2}\theta \tan^2 \theta=\\ \tan^{n-2}\theta(\sec^2\theta-1)=\\ \tan^{n-2}\theta\sec^2\theta-\tan^{n-2}\theta \end{gather*}$$ so $$\int\tan^2\theta\ d\theta=\int\tan^{n-2}\theta\sec^2\theta\ d\theta-\int\tan^{n-2}\theta\ d\theta$$ use a [itex]u=\tan\theta$$ substitution and you have
$$I_n(x)=\int^{u(x)} u^{n-2}\ du-I_{n-2}(x)$$

and maybe you can take it from there?

Last edited: Dec 2, 2003
4. Dec 2, 2003

### joc

BLUE_CHIP: you're taking Further Maths at 16? as in the A-level subject? that's pretty impressive...

5. Dec 2, 2003

### BLUE_CHIP

Well, I'm taking the A-level this year but I had done all the single Maths before so my teacher said that we should start on P4 and P5 so HeyHo. Fun and games...

6. Dec 4, 2003

### joc

heh that's cool. then you'll be like, a match for some of the more accelerated people in the US :P enjoy yourself.

7. Dec 4, 2003

### PrudensOptimus

Lame, just another "Hey look I'm 16 and I'm integrating, but I don't know what to do, pls help and btw, I'm 16, say I'm cool pls" thread...

STFU pls. thanks.

8. Dec 4, 2003

### franznietzsche

dude what is your problem? get off the guy's case. Seriously, so what if he mentions he's sixteen and integrating, for most people (excepting the true geniuses) thats something of an accomplishment. so lay off with being such an ass to someone jsut looking for help.

9. Dec 5, 2003

### joc

actually integration in itself isn't particularly impressive (most people around me learn it at 16); in fact i just recalled that taking Further Math at 16-17 is actually normal and not exceptional, so i take my compliment back.

no offence blue_chip :)

10. Dec 5, 2003

### franznietzsche

well i live in california, and here about 80 (out of 3000) students a year take AP calculus, while about 70% can't pass a test on simple algebra and geometry. So for this educationally challenged state it is something of an accomplishment. And even if it isn't its still no reason to go off on him.

11. Dec 5, 2003

### himanshu121

Well guys Here in India we have these kind of functions and problems when we are 17
and calculus is dominating feature. I must say it is compulsory here.