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Nilai dari 0 ∫ ​ 3 π ​ ​ ( sin x cos x ) d x = ...

Nilai dari  = ...

  1. begin mathsize 12px style 3 over 8 end style

  2. begin mathsize 12px style 4 over 8 end style

  3. begin mathsize 12px style 5 over 8 end style

  4. begin mathsize 12px style 6 over 8 end style

  5. 1

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Y. Laksmi

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

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Jawaban

 begin mathsize 12px style stack integral for 0 of with begin inline style straight pi over 3 end style on top open parentheses sin x space cos x close parentheses d x equals 3 over 8 end style

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Pembahasan

Misal: u(x) = sin x du = cosx dx Maka Jadi,

begin mathsize 12px style integral f open parentheses g open parentheses x close parentheses close parentheses times g to the power of 1 open parentheses x close parentheses d x equals integral f left parenthesis u right parenthesis d u equals F left parenthesis u right parenthesis plus C equals F open parentheses g open parentheses x close parentheses close parentheses plus C integral from 0 to begin inline style straight pi over 3 end style of left parenthesis sin x space cos x right parenthesis d x end style

Misal:

u(x) = sin x

du = cosx dx

Maka

begin mathsize 12px style stack integral for 0 of with begin inline style straight pi over 3 end style on top open parentheses sin x space cos x close parentheses d x equals stack integral for 0 of with begin inline style straight pi over 3 end style on top u d u equals open parentheses 1 half u squared close parentheses subscript 0 superscript begin inline style straight pi over 3 end style end superscript equals open parentheses 1 half sin squared x close parentheses subscript 0 superscript begin inline style straight pi over 3 end style end superscript equals open parentheses 1 half left parenthesis sin 60 right parenthesis squared close parentheses minus open parentheses 1 half left parenthesis sin 0 right parenthesis squared close parentheses equals 1 half cross times 3 over 4 minus 0 equals 3 over 8 end style

Jadi, begin mathsize 12px style stack integral for 0 of with begin inline style straight pi over 3 end style on top open parentheses sin x space cos x close parentheses d x equals 3 over 8 end style

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