ellemay96
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The question asks: Find G'(x) when G(x)= \int^(lnx)_a arcsin(t)/(2+sin(t))\ dt .

Apparently the solution is G'(x)=((arcsin(x))/(2+x))/x , but this doesn't seem right to me. I thought you would replace (2+x) with (2+sin(x)). Can someone please clarify? Thanks

(edit: sorry the limits of the integral are between ln(x) (upper) and a. I can't seem to change it.)
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poorform
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\displaystyle \int_{a}^{ln(x)}\frac{arcsin(t)}  {2+sin(t)}~dt

For anyone who wants to help.

Also I think you can just plug the limits into \displaystyle \frac{arcsin(t)}{2+sin(t)} by application of the FTC although that may well be wrong.
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DFranklin
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I don't agree with the answer either. (I think it's a mile off - about 3 separate corrections needed).

(Original post by davros)
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(Original post by ghostwalker)
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davros
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(Original post by DFranklin)
I don't agree with the answer either. (I think it's a mile off - about 3 separate corrections needed).

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Did you really want me to look at this monstrosity?

I can never do this sort of thing off the top of my head, so I headed for the Wikipedia definition - unless I've screwed up, I make the answer to be

\dfrac{arcsin(ln x)}{x(2 + \sin(ln x))}

- does that look about right?
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DFranklin
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(Original post by davros)
Did you really want me to look at this monstrosity?

I can never do this sort of thing off the top of my head, so I headed for the Wikipedia definition - unless I've screwed up, I make the answer to be

\dfrac{arcsin(ln x)}{x(2 + \sin(ln x))}

- does that look about right?
Yes, that's what I get too. Thanks.
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ellemay96
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(Original post by davros)
Did you really want me to look at this monstrosity?

I can never do this sort of thing off the top of my head, so I headed for the Wikipedia definition - unless I've screwed up, I make the answer to be

\dfrac{arcsin(ln x)}{x(2 + \sin(ln x))}

- does that look about right?
Thank you. I guess i'll get the university to correct it
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