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Ocr c4 question, jan 2012

Hi everyone, have a question on integration by substitution. Can anyone explain to me how to integrate this (not sure how to "remove" the sinx in particular). Sorry about the poor picture quality, hope you can still see it properly!
Thanks in advance :smile:

ImageUploadedByStudent Room1371314111.865350.jpg

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Reply 1

Barcelona'99

Original post by daisyrchds

Posted from TSR Mobile

if u = cos x
then du/dx = -sin x
and dx = du/-sinx

Replace the cos x and the dx in your integral to give:
integral of (u sin^3x) du/-sinx

One of the sinx cancels. Leaving (put minus sign out at the front)
- integral of (u sin^2) du

you know that u=cos x
therefore u^2 = cos^2x
take both sides away from 1
1-u^2 = sin^2x
Replace this in the integral
Change limits as well, should be okay from there