Saya mau tanya,mohon jawabannya....
integral,batas atas π,batas bawahnya 0, cos x e pangkat sin,dipangkatkan lagi x, ditanya dx???
integral,batas atas π,batas bawahnya 0, cos x e pangkat sin,dipangkatkan lagi x, ditanya dx???
Takamori37
Asumsi integral:
![\int_0^\pi \cos x e^{\sin x}\, dx \\ $Misalkan:$ \\ u=\sin x \\ du=\cos x\, dx \\ $Sehingga:$ \\ \int_{\sin0}^{\sin \pi} e^u\, du=e^u]_{\sin0}^{\sin\pi} \\ $Substitusi ulang:$ \\ \int_0^\pi \cos x e^{\sin x}\, dx =e^{\sin x}]_0^\pi \\ \int_0^\pi \cos x e^{\sin x}\, dx =e^{\sin\pi}-e^{\sin 0} \\ \int_0^\pi \cos x e^{\sin x}\, dx =e^0-e^0 \\ \int_0^\pi \cos x e^{\sin x}\, dx =1-1 \\ \int_0^\pi \cos x e^{\sin x}\, dx =0](https://tex.z-dn.net/?f=%5Cint_0%5E%5Cpi+%5Ccos+x+e%5E%7B%5Csin+x%7D%5C%2C+dx+%5C%5C+%24Misalkan%3A%24+%5C%5C+u%3D%5Csin+x+%5C%5C+du%3D%5Ccos+x%5C%2C+dx+%5C%5C+%24Sehingga%3A%24+%5C%5C+%5Cint_%7B%5Csin0%7D%5E%7B%5Csin+%5Cpi%7D+e%5Eu%5C%2C+du%3De%5Eu%5D_%7B%5Csin0%7D%5E%7B%5Csin%5Cpi%7D+%5C%5C+%24Substitusi+ulang%3A%24+%5C%5C+%5Cint_0%5E%5Cpi+%5Ccos+x+e%5E%7B%5Csin+x%7D%5C%2C+dx+%3De%5E%7B%5Csin+x%7D%5D_0%5E%5Cpi+%5C%5C+%5Cint_0%5E%5Cpi+%5Ccos+x+e%5E%7B%5Csin+x%7D%5C%2C+dx+%3De%5E%7B%5Csin%5Cpi%7D-e%5E%7B%5Csin+0%7D+%5C%5C+%5Cint_0%5E%5Cpi+%5Ccos+x+e%5E%7B%5Csin+x%7D%5C%2C+dx+%3De%5E0-e%5E0+%5C%5C+%5Cint_0%5E%5Cpi+%5Ccos+x+e%5E%7B%5Csin+x%7D%5C%2C+dx+%3D1-1+%5C%5C+%5Cint_0%5E%5Cpi+%5Ccos+x+e%5E%7B%5Csin+x%7D%5C%2C+dx+%3D0 "\int_0^\pi \cos x e^{\sin x}\, dx \\ $Misalkan:$ \\ u=\sin x \\ du=\cos x\, dx \\ $Sehingga:$ \\ \int_{\sin0}^{\sin \pi} e^u\, du=e^u]_{\sin0}^{\sin\pi} \\ $Substitusi ulang:$ \\ \int_0^\pi \cos x e^{\sin x}\, dx =e^{\sin x}]_0^\pi \\ \int_0^\pi \cos x e^{\sin x}\, dx =e^{\sin\pi}-e^{\sin 0} \\ \int_0^\pi \cos x e^{\sin x}\, dx =e^0-e^0 \\ \int_0^\pi \cos x e^{\sin x}\, dx =1-1 \\ \int_0^\pi \cos x e^{\sin x}\, dx =0")
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coriyoona
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