anonymous
  • anonymous
whats the definite integral from pi/6 to pi/4 of -x/(1-x^4)^1/2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
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.
anonymous
  • anonymous
ok, thanks a lot
myininaya
  • myininaya
did you try a trig substitution? that might work

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anonymous
  • anonymous
that's not true, it's a identity it's the inverse sin identity.
anonymous
  • anonymous
thats what i'm supposed to do, but i'm extremely lost. What do you mean it's the inverse sin identity?
anonymous
  • anonymous
\[-\frac{1}{2}\sin^{-1} (x^2)dx\] from pi/6 to pi/4
anonymous
  • anonymous
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
anonymous
  • anonymous
Oh god lol I feel like a dolt. Yes it's an inverse trig ID. Sorry
myininaya
  • myininaya
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anonymous
  • anonymous
whoa myininaya, did you just do that? lols props!
anonymous
  • anonymous
i dont think we're there yet. we're supposed to substitute and let u=x^2
myininaya
  • myininaya
yes lol
anonymous
  • anonymous
then how are you going to integrate the u^2 without a u on the outside...
myininaya
  • myininaya
they are not hard to derive. it is harder for me to memorize more stuff so i derive it everytime
myininaya
  • myininaya
? what u?
anonymous
  • anonymous
i dont know, thats why im so confused
anonymous
  • anonymous
myininaya- the hint that came with the question said to let u=x^2
anonymous
  • anonymous
it's going to get really messy...but you can try u - subbing again....
myininaya
  • myininaya
why let u=x^2 when you can let cos( pheta)=x^2
myininaya
  • myininaya
where is the hint you guys are talking about? don't do that way. lol. hints can be gross
anonymous
  • anonymous
LOLOLOLOLL go myininaya
myininaya
  • myininaya
i mean we can try, but I don't see why
anonymous
  • anonymous
its number 2 on the first page
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myininaya
  • myininaya
have you done trig substitution before?
anonymous
  • anonymous
nope
myininaya
  • myininaya
ok let me think about then
anonymous
  • anonymous
ok, thanks for helping me with this
anonymous
  • anonymous
i think i understand what your book wants it want's u sub and trig id give me a min to type this out
anonymous
  • anonymous
\[-\int\limits_{\pi/6}^{\pi/4}\frac{x}{\sqrt{1-x^4}}dx\] 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 \[-\frac{1}{2}\sin^{-1} (x^2)\]
myininaya
  • myininaya
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
myininaya
  • myininaya
right
anonymous
  • anonymous
doing it this way satisfies the hint of using u-sub ^_^
anonymous
  • anonymous
ok, so then what do i do with the limits? f(b)-f(a)?
myininaya
  • myininaya
just plug them into the antiderivative
anonymous
  • anonymous
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
myininaya
  • myininaya
putting them is the easy part
anonymous
  • anonymous
haha dont apologize, thanks for all your help, you guys saved me :)
anonymous
  • anonymous
cheers good luck
myininaya
  • myininaya
deriving them is fun too so if you don't want to memorize junk learn to derive them
anonymous
  • anonymous
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
anonymous
  • anonymous
hahaha i'll remember that
myininaya
  • myininaya
lol right. i have to derive alot of stuff because my memory sucks
anonymous
  • anonymous
are you an engineering major?
myininaya
  • myininaya
no im a math major
anonymous
  • anonymous
fun stuff, good luck with everything
anonymous
  • anonymous
i'm computer engineering major
anonymous
  • anonymous
got one right :D
myininaya
  • myininaya
computer engineering is dreamy im going to start my phd next semester and i picked to do a research in the theory of cryptography
anonymous
  • anonymous
that sounds interesting and hard at the same time, good luck
anonymous
  • anonymous
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
myininaya
  • myininaya
lol i think i want to date it lol
anonymous
  • anonymous
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 -_-
anonymous
  • anonymous
which class? I'm a Computer Science major, love programming.
anonymous
  • anonymous
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...
anonymous
  • anonymous
oh matlab is nuts. Used a ton for scientific programming.

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