Try Out Ujian Nasional Matematika IPA Paket 6 Buku Sukino no 39

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Paket 6

39. Nilai dari ₀ഽ^π/6 sin (x + π/3) cos (x +  π/3) dx sama dengan ...

a. - 0,250

b. -0,125

c. 0,125

d. 0,250

e. 0,375

Jawaban : C

₀ഽ^π/6 sin (x + π/3) cos (x +  π/3) dx

sifat trigonometri :

sin 2A = 2 sin A cos A

sin A cos A = 1/2 sin 2A

₀ഽ^π/6 1/2 sin 2(x + π/3) dx

= 1/2 ₀ഽ^π/6 sin 2(x + π/3) dx

= 1/2 . ₀ഽ^π/6 sin (2x + 2π/3) dx

= 1/2 . [ - 1/2 cos (2x + 2π/3) + C] ₀^π/6

= 1/2 . - 1/2 . (cos 2(π/6) + 2π/3 - cos 2 (0) - 2π/3))

= - 1/4 . (cos π/3 - cos 0)

= - 1/4 . (1/2 - 1)

= - 1/4 . - 1/2

= 1/8

= 0,125

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