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C3 help!

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 :smile:

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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 :smile:

Attachment not found.
Sorry! I'm new to this so didn't realise the attachment wasn't working! :smile: Thank you!
Untitled.docx53.0KB
Original post by science_geeks
Sorry! I'm new to this so didn't realise the attachment wasn't working! :smile: 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 u(u−1)\sqrt{u}(u-1) and using the fact that u=u1/2\sqrt{u} = u^{1/2}
Ah I see! That makes sense now. Thank you for the help!! :smile:

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 u(u−1)\sqrt{u}(u-1) and using the fact that u=u1/2\sqrt{u} = u^{1/2}
Original post by science_geeks
Sorry! I'm new to this so didn't realise the attachment wasn't working! :smile: 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.
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! :smile:

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