trig (1 Viewer)

Arithela · Jul 13, 2008

whats the difference between sin²x and (sinx)²
and how would you differentiate/integrate them?

karnage · Jul 13, 2008

There is no difference between them.

You use the chain rule to differentiate that

And to integrate you change it to 1/2 (1 - cos2x) and then integrate as normal.

Arithela · Jul 13, 2008

thanks, would the answer be 2cos²x(sinx) by differentiating?

Aerath · Jul 14, 2008

3unitz said:
y = (sin x)^2

dy/dx = 2 (sin x) (cos x)

Just wondering, when you get answers like that - do you need to go the next step further and say dy/dx = sin2x?

lyounamu · Jul 14, 2008

Aerath said:
Just wondering, when you get answers like that - do you need to go the next step further and say dy/dx = sin2x?

Well, I was going to write that 3 hours ago when I first looked at this post. But I don't think it will be necessary even though I will do it just in case.

vds700 · Jul 14, 2008

Aerath said:
Just wondering, when you get answers like that - do you need to go the next step further and say dy/dx = sin2x?

not in 2 unit, bit in extension 1, yes

Arithela · Jul 14, 2008

ok how would u integrate that then?

midifile · Jul 14, 2008

Arithela said:
ok how would u integrate that then?

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Integrate sin<sup>2</sup>x? You only have to know how to do that if you do 3 unit

lyounamu · Jul 14, 2008

Arithela said:
ok how would u integrate that then?

cos 2x = 1-2sin^2(x)
2sin^2(x) = 1-cos2x
sin^2(x) = (1-cos2x)/2

When you try to integrate sin^2(x), you substitue (1-cos2x)/2 for the value of sin^2(x) because sin^2(x) can not be integreated. (or very hard to be integrated).

So you get 1/2x - 1/4sin2x + c

Arithela · Jul 14, 2008

oh its only in 3 unit, thanks though!

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