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Integral Calculus

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 Joined: 6 Jan 2009 Post: 20
6 Jan 2009 22:28:42 IST
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integration of root of (tan^2 x+2)
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Integral Calculus

integration of root of (tan^2 x+2)

Blazing goIITian

Joined: 10 Jun 2007
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6 Jan 2009 22:30:19 IST
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root of this quantity would be simply tan(x+2)... please check the question

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6 Jan 2009 22:35:12 IST
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is it - Log| | +k

New kid on the Block

Joined: 6 Jan 2009
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6 Jan 2009 23:38:55 IST
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integration of : root of {tan^2 (x) +2};
please give me correct as with explanation

New kid on the Block

Joined: 2 Jan 2009
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8 Jan 2009 20:27:30 IST
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hello...........

{tan^2x+2}^1/2={sec^2x+1}^1/2

={sec^2x+1}/{sec^2x+1}^1/2

=sec^2x/{sec^2x +1}^1/2 + 1/{sec^2x+1}^1/2

=sec^2x/{tan^2x +2}^1/2     + cosx/{1+cos^2x}^1/2

=sec^2x/{tan^2x +2}^1/2  + cosx/{2-sin^2x}^1/2 =f{x}

now for integral f{x}dx   for first term put tanx =t ,for second term put sinx =t and integrate

am i correct ???????????????

Cool goIITian

Joined: 27 Dec 2008
Posts: 82
9 Jan 2009 23:47:35 IST
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integration of root of (tan^2 x+2)

let the thing inside the integral=t^2...make this substituton and solve furthur to get...

t^2 dt/ (t^2 -2)^1/2  * (t^2 -1)...

now make a substitution as...(t^2 -2)=u^2...

sove the expression to get ... (u^2 + 2)^(1/2 )/ u^2 +1..

now rationalize the root expression and divide Nr BY Dr to get a simplified expression which can be integrated easily...

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