anonymous
  • anonymous
integrating from sinx to 1 (t^2 f(t)dt=1-sinx for all xE R ,then f(1/sq.root(3))
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
Try using the Equation button in the bottom.
anonymous
  • anonymous
Is it \[\int\limits_{\sin x}^{1}t^2f(t) dt=1-\sin x?\]
anonymous
  • anonymous
Are you there?

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anonymous
  • anonymous
Just tell me if what I wrote there is what you're asking about :)
anonymous
  • anonymous
yaa
anonymous
  • anonymous
Good. Do you know the fundamental theorem of calculus?
anonymous
  • anonymous
i dunn mayb
anonymous
  • anonymous
Hmm. I will start by taking the derivative of both sides. Taking the derivative of the integral can be done using: \[\int\limits_{a}^{g(x)}f(t)dt=f(g(x)).g'(x)\]
anonymous
  • anonymous
Sorry write before the integral d/dx
anonymous
  • anonymous
but y
anonymous
  • anonymous
oh i gotta
anonymous
  • anonymous
\[{d \over dx}\int\limits_{\sin x}^{1}t^2f(t)dt={d \over dx}(1-\sin x)\]
anonymous
  • anonymous
You are leaving?
anonymous
  • anonymous
no
anonymous
  • anonymous
You got the formula I wrote above?
anonymous
  • anonymous
yaa but then with this we hav to find f(\[ 1/\sqrt{3}\])
anonymous
  • anonymous
I know.. We have to find f(x) first.
anonymous
  • anonymous
oh
anonymous
  • anonymous
It will take just two more steps.
anonymous
  • anonymous
k
anonymous
  • anonymous
\[\implies -(\sin^2 x)f(\sin x)\cos x=-\cos x \implies \cos x(- \sin^2 x f(\sin x)+1)=0\]
anonymous
  • anonymous
It follows that: cos x=0 or \[\sin^2 x f(\sin x)=1 \implies f(\sin x)={1 \over \sin^2 x}\]
anonymous
  • anonymous
Now to find the value of f(1/sqrt(3)).. put x=pi/3
anonymous
  • anonymous
k
anonymous
  • anonymous
Sorry.. not pi/3, just substitute x=sin^-1(1/sqrt(3))you will get:
anonymous
  • anonymous
bot acc to formula g(x) =1 then y we substitute sinx
anonymous
  • anonymous
\[f(\sin(\sin^{-1}(1/\sqrt3))=f(1/\sqrt3)={1 \over \sin^2(\sin^{-1}{1\over \sqrt3})}={1 \over 1/3}=3\]
anonymous
  • anonymous
Do you have the answer?
anonymous
  • anonymous
you know that sin(arcsinx)=x, right? because arcsin just "undoes" the sin since it's its inverse.
anonymous
  • anonymous
3
anonymous
  • anonymous
Ok.. that's what I got and showed above. I hope the steps are clear, and make sense to you.
anonymous
  • anonymous
thnks
anonymous
  • anonymous
r u teacher
anonymous
  • anonymous
No. I am a student.
anonymous
  • anonymous
quit intelligent
anonymous
  • anonymous
Thanks!! :)
anonymous
  • anonymous
passed out 12 this yr
anonymous
  • anonymous
What?
anonymous
  • anonymous
hav u passed out 12 this yr?
anonymous
  • anonymous
hav u passed out 12 this yr?
anonymous
  • anonymous
I don't know what that means.

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