Mohon bantu jawab ,masih belum tau bagaimana cara penyelesaiannya. nomor 1 - 2
Matematika
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Pertanyaan
Mohon bantu jawab ,masih belum tau bagaimana cara penyelesaiannya. nomor 1 - 2
1 Jawaban
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1. Jawaban DB45
integral
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{ sec x = 1/cos x}
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(π/2...π/4) ∫ cos x sec³ dx dx =
= (π/2..π/4) ∫ cos x (1/cos ³ x) dx
= (π/2..π/4) ∫ 1/cos² x dx
= (π/2 ..π/4) ∫ sec² x dx
= [tan x ](π/2 ...π/4)
= tan π/2 - tan π/4
= eror
2. ∫ ln² (x) dx
dengan parsial ∫ u dv = uv - ∫v du
u = ln² (x) --> du = (2 ln x)/x
dv = dx --> v = ∫dx = x
∫ ln² (x) dx = x ln² x - ∫ x { 2 ln x )/ x) dx + c
= x ln² x - ∫ 2 ln x dx + c
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cari dulu ∫ 2 ln x dx , dgn parsial ∫ f dg = fg - ∫ g df
f = 2 ln x , df = 2/x
dg = dx --> g = ∫ dx = x
∫2 ln x dx = 2x ln x - ∫ x (2/x) dx
∫ 2 ln x dx = 2(x). ln (x) - 2x
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∫ ln² (x) dx = x ln² (x) - 2x ln x + 2x + c