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#1 Posted 4:05pm 22-03-10 delhi mathematics paper (BOARDS)The question that said [sin x + cos x] / [sqrt]sin2x[/sqrt] this function had to be integrated with limits (pi/6) to (pi/3) |
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#2 Posted 4:06pm 22-03-10 Re: delhi mathematics paper (BOARDS)all the delhi people and all india are requested to solve this question. any more question can be added but make sure to write teh complete question. |
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#3 Posted 4:27pm 22-03-10 Re: delhi mathematics paper (BOARDS)the given is equalt to [im]http://codecogs.izyba.com/gif.latex?\int\frac{\sqrt{tanx}+\sqrt{cotx}}{\sqrt{2}}dx[/im] this can be eva;uated easily by taking tanx=t and cotx=v
"lead,follow or get out of the way" Edited on 4:29pm 22-03-10 |
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#4 Posted 4:42pm 22-03-10 Re: delhi mathematics paper (BOARDS)Integral is [im]http://codecogs.izyba.com/gif.latex?\frac{1}{\sqrt{2}}\int_{\pi%20/6}^{\pi%20/3}{\frac{sinx+cosx}{\sqrt{sinxcosx}}dx[/im] now put [im]http://codecogs.izyba.com/gif.latex?sinx%20-%20cosx%20=%20t%20\Rightarrow%20(cosx+sinx)dx=dt[/im] [im]http://codecogs.izyba.com/gif.latex?\Rightarrow%20(1-sin2x)%20=%20t^{2}%20\Rightarrow%20sin2x%20=%20t^{2}-1[/im] now substituting in integral we get [im]http://codecogs.izyba.com/gif.latex?\int_{\pi%20/6}^{\pi%20/3}{\frac{dt}{\sqrt{1-t^{2}}}}[/im] = sin [p]-1[/p](sinx - cosx) + c now substitute the limits u will get the ans.
In every loss, in every lie, in every truth that you'd deny
And each regret and each goodbye was a mistake too great to hide
And your voice was all I heard that I get what I deserve
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#5 Posted 7:45pm 22-03-10 Re: delhi mathematics paper (BOARDS)Kaustab the way you're doing it, it'll be quite long even though it's an NCERT example. The easier way is to apply the substitution Manmay has. And Manmay, after changing the integral variable to t we [b]change the limits[/b] too. Your answer won't be in terms of x, it will be in terms of t. Little silly mistake..lol.
Self belief is such a peculiar thing. As long as you have it, nothing can stop you, you feel invulnerable. But once it's gone, nothing can bring you up from the "I'm-useless" state you end up in. Edited on 7:46pm 22-03-10 |
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#6 Posted 7:52pm 22-03-10 Re: delhi mathematics paper (BOARDS)[b]i thin manmay is right der limits may be kept same if we express ans at last in terms of x and not t [/b]
Edited on 7:58pm 22-03-10 |
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#7 Posted 7:58pm 22-03-10 Re: delhi mathematics paper (BOARDS)Jo mujhe sikhaya gaya hai I am going as per that SR....well I don't know, lets see [12]
Self belief is such a peculiar thing. As long as you have it, nothing can stop you, you feel invulnerable. But once it's gone, nothing can bring you up from the "I'm-useless" state you end up in. |
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#8 Posted 7:58pm 22-03-10 Re: delhi mathematics paper (BOARDS)@ pritish i did that for it would be easy, keeping limits same when we get final answer in terms of t we substitute t ' s value and use limits changing limits would be ime taking. but i should have done that here. sorry for the mistake.
In every loss, in every lie, in every truth that you'd deny
And each regret and each goodbye was a mistake too great to hide
And your voice was all I heard that I get what I deserve
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