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    Find the exact value of  \displaystyle \int_{0}^{\pi /4} \sqrt{\tan x } \ dx .
    I'm having a bit of trouble with this one.
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    (Original post by Ano9901whichone)
    Find the exact value of  \displaystyle \int_{0}^{\pi /4} \sqrt{\tan x } \ dx .
    I'm having a bit of trouble with this one.
    Start with u^2 = \tan x then post all your working if you get stuck.
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    Dear Friend,
    here is a fully worked solution.
    Best,
    Yahia Ezzat
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    (Original post by Yahia Ezzat)
    Dear Friend,
    here is a fully worked solution.
    Best,
    Yahia Ezzat
    Is this c4 alevel maths?
    I think you did aomething wrong btw
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    (Original post by Yahia Ezzat)
    Dear Friend,
    here is a fully worked solution.
    Best,
    Yahia Ezzat
     \displaystyle sec^2x isnt a constant wrt u
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    (Original post by Ano9901whichone)
    Find the exact value of  \displaystyle \int_{0}^{\pi /4} \sqrt{\tan x } \ dx .
    I'm having a bit of trouble with this one.
    Integral of sqrt(tan(x)) is notoriously horrible. u^2 = tan x is the natural sub but you end up having to integrate something with denominator 1+u^4 which is a bit nasty...

    The choice of limits makes me wonder if you can possibly do something quicker by looking at u = pi/2 - x and combining, but looking at the actual solution (via Wolfram) I'm not sure there is going to be any good trick here.
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    (Original post by Yahia Ezzat)
    Dear Friend,
    here is a fully worked solution.
    Best,
    Yahia Ezzat
    We have Forum Rules (pinned to the top of the Maths Forum) that ask you not to post full solutions. Posting wrong solutions is even more unhelpful.
 
 
 
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