Integration - year 13 Watch

hl1479
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How do u integrate this??
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hl1479
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Notnek
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(Original post by hl1479)
for D
You can rewrite this as

\sin x \left(\cos x\right)^{-5} and notice that \sin x is nearly the derivative of \cos x.

Does that help or are you still unsure?
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hl1479
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(Original post by Notnek)
You can rewrite this as

\sin x \left(\cos x\right)^{-5} and notice that \sin x is nearly the derivative of \cos x.

Does that help or are you still unsure?
Hmmm im still not too sure - where do i go from there??
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Notnek
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(Original post by hl1479)
Hmmm im still not too sure - where do i go from there??
When you see a function/derivative pattern like this (you really need to look out for them) then you can either substitute the function - in this case u=\cos x and the \sin x will cancel. Or you can use "recognition" methods if you're comfortable with them.
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hl1479
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Ohhhh okay i see - how do u integrate the cos^5x?
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Notnek
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(Original post by hl1479)
Ohhhh okay i see - how do u integrate the cos^5x?
You don't need to integrate that. Which method (out of the two I gave you) are you using? If you're using substitution then please post your working.
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hl1479
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(Original post by Notnek)
You don't need to integrate that. Which method (out of the two I gave you) are you using? If you're using substitution then please post your working.
I was using substitution - im out at the moment I’ll send it abit later. But can u not use u=cos^5 then differentiate that?
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Notnek
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(Original post by hl1479)
I was using substitution - im out at the moment I’ll send it abit later. But can u not use u=cos^5 then differentiate that?
That won’t work as a substitution. But considering the derivative of cos^(-4)x is one way to do this question.

If you’re trying to use “recognition” methods then you always add 1 to the power and consider its derivative.

If you’re trying to use substitution then you should substitute u=cos(x).
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hl1479
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(Original post by Notnek)
That won’t work as a substitution. But considering the derivative of cos^(-4)x is one way to do this question.

If you’re trying to use “recognition” methods then you always add 1 to the power and consider its derivative.

If you’re trying to use substitution then you should substitute u=cos(x).
Ohhh okay ill try this when i get home! Thank uu
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