Monday, August 30, 2010

Best2!

Ha..kali ni post menarik sikit! Tg Masyitah tanya pasal soalan ni.Harap dapat faham jalan kerja ni ^_^


Soalan : ∫ sin(ln x) dx

Let w = ln x

dw = dx/x

x dw = dx

so jadilah,

x sin w dw

Sbb x = e^w(tgk kat bawah macam mana dapt ni),maka

e^w sin w dw

Guna ibp

Let u = sin w

du = cos w dw

dv = e^w dw

v = e^w

uv - ∫ v du = e^w sin w - e^w cos w dw à ibp lg sekali

e^w cos w dw

Let u = cos w dv = e^w dw

du = -sin w dw v = e^w

e^w cos w dw = e^w cos w + ∫ e^w sin w dw

(bila dah sama dgn soalan,stop gune ibp)

e^w sin w dw = e^w sin w – e^w cos w - ∫ e^w sin w dw

e^w sin w dw + ∫ e^w sin w dw = e^w sin w – e^w cos w

2∫ e^w sin w dw = e^w sin w – e^w cos w

e^w sin w dw = (e^w sin w – e^w cos w)/2

Tukar balik w = ln x

∫ x sin(ln x) dx/x = (x sin(ln x) – x cos(ln x))/2

sin(ln x) dx = (x sin(ln x) – x cos(ln x))/2

Done!


e^w = e^ln x

e^w = x

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