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Ask iit jee aieee pet cbse icse state board community Community Discussion Question: integrate
Forum Index -> Integral Calculus like the article? email it to a friend.  
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[Post New]20 Feb 2008 12:59:12 IST
    Subject: integrate
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avi_1214545 (974)

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dx/(sec^2 x   +   tan^2 x)
Na pine ka shouk tha na pilane ka shonk tha. Hume to sirf NAZREIN milane ka shonk tha. Par kya karen hum nazre hi unse mila baithe jinhe nazron se PILANE ka shonk tha.
    
[Post New]20 Feb 2008 13:08:04 IST
    Subject: Re:integrate
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rhd92781 (686)

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sec2x+tan2x = 1+2tan2x
 
dx/(sec^2 x   +   tan^2 x)
=[ ][ ] (1+tan2x)/(1+tan2x)(1+2tan2x) dx
= sec2x dx /(1+tan2x)(1+2tan2x)
 
let tanx = t
sec2x dx = dt
integral becomes
dt / (1+t)(1+2t)
=  2 dt/(1+2t) -  dt / (1+t)
 
integrate and put t=tanx bak
<TABLE CELLSPACING="1" CELLPADDING="1" BORDER="0">
<TR><TD>


<DIV ALIGN="right">Animated Letters</DIV></TD></TR></TABLE>

I am only one,
But still I am one.
I cannot do everything,
But still I can do something;
And because I cannot do everything
I will not refuse to do the something that I can do.
- Edward Everett Hale
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[Post New]20 Feb 2008 13:08:37 IST
    Subject: Re:integrate
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raulrag009 (1194)

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Multiply by sec2x in numerator and denominator
 
I =sec^2xdx / (1+tan2x)(1+2tan2x)
 
Put tanx=t
      sec^2xdx=dt
I = dt/(1+t2)(1+2t2)
 
Let
 
1/(1+t2)(1+2t2)  =  At+B/1+t^2   +   Ct+D/1+2t^2 
 
u can solve further by comparing
 
Ans is
tan-1(2tanx)  -  tan-1(tanx) +C
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[Post New]20 Feb 2008 13:09:59 IST
    Subject: integrate
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rhd92781 (686)

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yeah sory...it wud be
dt / (1+t^2)(1+2t^2)
<TABLE CELLSPACING="1" CELLPADDING="1" BORDER="0">
<TR><TD>


<DIV ALIGN="right">Animated Letters</DIV></TD></TR></TABLE>

I am only one,
But still I am one.
I cannot do everything,
But still I can do something;
And because I cannot do everything
I will not refuse to do the something that I can do.
- Edward Everett Hale
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[Post New]20 Feb 2008 13:11:29 IST
    Subject: integrate
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avi_1214545 (974)

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yeah...thanxx
Na pine ka shouk tha na pilane ka shonk tha. Hume to sirf NAZREIN milane ka shonk tha. Par kya karen hum nazre hi unse mila baithe jinhe nazron se PILANE ka shonk tha.
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