p3 integration Watch

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Jackal123
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#1
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#1
Integrate sin x cos^4 x

Please can someone tell me what method to use and how it can be integrated.
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RichE
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#2
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#2
Substitution with u = cosx
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Jackal123
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how do you know that?
And where would I go from there?

Cheers
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Font
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#4
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(Original post by Jackal123)
Integrate sin x cos^4 x

Please can someone tell me what method to use and how it can be integrated.
integrate it using "recognition"....answer by looking at it is -(1/5) * cos^5 x, or you can use a substituion of u = sin x.

The easiest method is to look at it. you know the rule for differentiating something like sin ^ n x and cos ^ n x...from standard results. Apply the reverse principle to your question, and bingo, you have it...hope it helps

Phil
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Newton
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f(x)=(sinx)((cosx)^4)

INTf(x)dx

Let u=cosx

f(x) then becomes f(u) as:

f(x)=(-(du/dx))(u^4)dx

dx cancel:

Therefore:

-INT(u^4)du

=>=-(1/5)(u^5)+C

*u=cosx

=>=-(1/5)((cosx)^5)

Newton.
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Nima
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#6
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(Original post by Jackal123)
Integrate sin x cos^4 x dx
Int. sinx.cos^4x dx. = - Int. (-sinx).(cosx)^4 dx. = -(cos^5x)/5 + k

Use: Int. f ' (x). [f(x)]^n dx = {[f(x)]^(n + 1)}/(n + 1) + k

Nima
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Jackal123
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What method would I use to integrate cosec 2x cot 2x ?

Please just tell me what method to use and then i will try the rest.

cheers
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RichE
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#8
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(Original post by Jackal123)
What method would I use to integrate cosec 2x cot 2x ?

Please just tell me what method to use and then i will try the rest.

cheers
Rewrite it in terms of sin2x's and cos2x's and use a substitution similar to the previous example.
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