whats the definite integral from pi/6 to pi/4 of -x/(1-x^4)^1/2

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whats the definite integral from pi/6 to pi/4 of -x/(1-x^4)^1/2

Mathematics
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You cannot do this by hand because letting u=1-x^4 its derivative would equate -4x^3 dx, which cannot be substituted into the equation. To find the result, type in the equation into y= on your calculator. Then go 2ND->Calc (top row of buttons) and hit #7 for integration. It will graph the function, and then ask for a lower and upper bound which is obviously the limits you provided.
ok, thanks a lot
did you try a trig substitution? that might work

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that's not true, it's a identity it's the inverse sin identity.
thats what i'm supposed to do, but i'm extremely lost. What do you mean it's the inverse sin identity?
\[-\frac{1}{2}\sin^{-1} (x^2)dx\] from pi/6 to pi/4
you can derive it, but most teachers (even in college) do not require it most teachers don't even require you to know them but some want you to memorize them that's the only way to recognize them that integral is the derivative of the inverse sin function
Oh god lol I feel like a dolt. Yes it's an inverse trig ID. Sorry
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whoa myininaya, did you just do that? lols props!
i dont think we're there yet. we're supposed to substitute and let u=x^2
yes lol
then how are you going to integrate the u^2 without a u on the outside...
they are not hard to derive. it is harder for me to memorize more stuff so i derive it everytime
? what u?
i dont know, thats why im so confused
myininaya- the hint that came with the question said to let u=x^2
it's going to get really messy...but you can try u - subbing again....
why let u=x^2 when you can let cos( pheta)=x^2
where is the hint you guys are talking about? don't do that way. lol. hints can be gross
LOLOLOLOLL go myininaya
i mean we can try, but I don't see why
its number 2 on the first page
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have you done trig substitution before?
nope
ok let me think about then
ok, thanks for helping me with this
i think i understand what your book wants it want's u sub and trig id give me a min to type this out
\[-\int\limits_{\pi/6}^{\pi/4}\frac{x}{\sqrt{1-x^4}}dx\] substitute u = x^2 and du = 2xdx \[-\frac{1}{2}\int\limits_{}^{}\frac{1}{\sqrt{1-u^2}}du\] now you use the trig id \[\int\limits_{}^{}\frac{1}{\sqrt{1-u^2}} = \sin^{-1} (u)\] so the answer is \[-\frac{1}{2}\sin^{-1} (u)\] sub x^2 back in \[-\frac{1}{2}\sin^{-1} (x^2)\]
i don't see how we can do this without trig identity or trig substitution. You have to know something about those trig integral stuff to do this problem
right
doing it this way satisfies the hint of using u-sub ^_^
ok, so then what do i do with the limits? f(b)-f(a)?
just plug them into the antiderivative
yup, since, we plugged x^2 back into u you just have to plug pi/6 and pi/4 into the answer that we got up there i stopped putting them in i'm sorry, i got lazy
putting them is the easy part
haha dont apologize, thanks for all your help, you guys saved me :)
cheers good luck
deriving them is fun too so if you don't want to memorize junk learn to derive them
lols the smart one is to learn to derive them, that way, you can never really forget because if you forget, just derive it again :D
hahaha i'll remember that
lol right. i have to derive alot of stuff because my memory sucks
are you an engineering major?
no im a math major
fun stuff, good luck with everything
i'm computer engineering major
got one right :D
computer engineering is dreamy im going to start my phd next semester and i picked to do a research in the theory of cryptography
that sounds interesting and hard at the same time, good luck
dreamy? what does that mean? and i like cryptography, at least i think i do...it's problem solving yes? i'm a freshman btw lols
lol i think i want to date it lol
lololls i love programming which involves a lot of problem solving i've only taken one programming class in college so far, and it wasn't special... i mean compared to the rest of my classes, it was awesome, but .. ehh -_-
which class? I'm a Computer Science major, love programming.
i learned matlab it's basically just a super calculator there are a lot of stuff that you can do with it but it's not really a language...
oh matlab is nuts. Used a ton for scientific programming.

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