Pertanyaan

Hasil ∫ 0 6 π sin 4 x . cos 2 x d x = ..... (UN 2013)

Hasil $\int_{0}^{\frac{π}{6}} sin 4 x . cos 2 x d x =$ ..... (UN 2013)

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Habis dalam

Klaim

A. Nadhira

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

$begin mathsize 12px style integral subscript 0 superscript straight pi over 6 end superscript sin space 4 x. cos 2 x space d x equals 1 half integral subscript 0 superscript straight pi over 6 end superscript 2 space sin 4 x. cos 2 x space d x equals 1 half integral subscript 0 superscript straight pi over 6 end superscript sin open parentheses 4 x plus 2 x close parentheses plus sin open parentheses 4 x minus 2 x close parentheses d x equals 1 half integral subscript 0 superscript straight pi over 6 end superscript sin open parentheses 6 x close parentheses plus sin open parentheses 2 x close parentheses d x equals 1 half open square brackets negative 1 over 6 cos open parentheses 6 x close parentheses minus 1 half cos open parentheses 2 x close parentheses close square brackets subscript 0 superscript straight pi over 6 end superscript equals 1 half open square brackets negative 1 over 6 left parenthesis cosπ minus cos 0 right parenthesis minus 1 half left parenthesis cos straight pi over 3 minus cos 0 right parenthesis close square brackets equals 1 half open square brackets negative 1 over 6 left parenthesis negative 1 minus 1 right parenthesis minus 1 half open parentheses 1 half minus 1 close parentheses close square brackets equals 1 half open square brackets negative 1 over 6 left parenthesis negative 2 right parenthesis minus 1 half open parentheses negative 1 half close parentheses close square brackets equals 1 half open square brackets 1 third plus 1 fourth close square brackets equals 1 half open square brackets fraction numerator 4 plus 3 over denominator 12 end fraction close square brackets equals 7 over 24 end style$