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anonymous
 5 years ago
integrating from sinx to 1 (t^2 f(t)dt=1sinx for all xE R ,then f(1/sq.root(3))
anonymous
 5 years ago
integrating from sinx to 1 (t^2 f(t)dt=1sinx for all xE R ,then f(1/sq.root(3))

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Try using the Equation button in the bottom.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Is it \[\int\limits_{\sin x}^{1}t^2f(t) dt=1\sin x?\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Just tell me if what I wrote there is what you're asking about :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Good. Do you know the fundamental theorem of calculus?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Hmm. 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
 5 years ago
Best ResponseYou've already chosen the best response.0Sorry write before the integral d/dx

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[{d \over dx}\int\limits_{\sin x}^{1}t^2f(t)dt={d \over dx}(1\sin x)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You got the formula I wrote above?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yaa but then with this we hav to find f(\[ 1/\sqrt{3}\])

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I know.. We have to find f(x) first.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It will take just two more steps.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\implies (\sin^2 x)f(\sin x)\cos x=\cos x \implies \cos x( \sin^2 x f(\sin x)+1)=0\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It follows that: cos x=0 or \[\sin^2 x f(\sin x)=1 \implies f(\sin x)={1 \over \sin^2 x}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Now to find the value of f(1/sqrt(3)).. put x=pi/3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Sorry.. not pi/3, just substitute x=sin^1(1/sqrt(3))you will get:

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0bot acc to formula g(x) =1 then y we substitute sinx

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[f(\sin(\sin^{1}(1/\sqrt3))=f(1/\sqrt3)={1 \over \sin^2(\sin^{1}{1\over \sqrt3})}={1 \over 1/3}=3\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Do you have the answer?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you know that sin(arcsinx)=x, right? because arcsin just "undoes" the sin since it's its inverse.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok.. that's what I got and showed above. I hope the steps are clear, and make sense to you.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0passed out 12 this yr

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hav u passed out 12 this yr?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hav u passed out 12 this yr?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I don't know what that means.
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