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    Hi everyone,

    I'm slightly confused with how to go from the U - substituted integral to taking out the 1/4 fraction. I can't figure out how they've got the 1/4 out in front with the fractional powers. Any help is really appreciated!

    Thank you in advance

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    (Original post by science_geeks)
    Hi everyone,

    I'm slightly confused with how to go from the U - substituted integral to taking out the 1/4 fraction. I can't figure out how they've got the 1/4 out in front with the fractional powers. Any help is really appreciated!

    Thank you in advance
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    Sorry! I'm new to this so didn't realise the attachment wasn't working! Thank you!
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    (Original post by science_geeks)
    Sorry! I'm new to this so didn't realise the attachment wasn't working! Thank you!
    There are two fractions with denominator of 2 being multiplied, so that's where the 1/4 comes from.

    The numerator is then just expanding \sqrt{u}(u-1) and using the fact that \sqrt{u} = u^{1/2}
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    Ah I see! That makes sense now. Thank you for the help!!

    (Original post by RDKGames)
    There are two fractions with denominator of 2 being multiplied, so that's where the 1/4 comes from.

    The numerator is then just expanding \sqrt{u}(u-1) and using the fact that \sqrt{u} = u^{1/2}
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    (Original post by science_geeks)
    Sorry! I'm new to this so didn't realise the attachment wasn't working! Thank you!
    If you multiply u^1/2 with the numerator, you get u^3/2 - u^1/2. Further, if you multiply du/2 (equivalent to 1/2 du) with the denominator you get 4.

    Consequently, the resulting integral would be u^3/2 - u^1/2 / 4. The 4 in the denominator is equivalent to multiplying the whole integral by 1/4. Therefore, you can take out 1/4.
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    (Original post by MoniC255)
    If you multiply u^1/2 with the numerator, you get u^3/2 - u^1/2. Further, if you multiply du/2 (equivalent to 1/2 du) with the denominator you get 4.

    Consequently, the resulting integral would be u^3/2 - u^1/2 / 4. The 4 in the denominator is equivalent to multiplying the whole integral by 1/4. Therefore, you can take out 1/4.
    Thanks for the explanation - it makes more sense now!
 
 
 
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