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# C3 help! watch

1. 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!

Attachment 729642
2. We can't see the question
3. (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!

4. Sorry! I'm new to this so didn't realise the attachment wasn't working! Thank you!
Attached Files
5. Untitled.docx (51.8 KB, 13 views)
6. (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 and using the fact that
7. 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 and using the fact that
8. (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.
9. (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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