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Pertanyaan

Nilai ∫ 0 2 x ​ ​ ( 2 sin 2 x cos x ) dx = ...

  1. 2 over 3

  2. fraction numerator 2 over denominator square root of 3 end fraction

  3. 1 third

  4. 1 plus square root of 3

  5. square root of 3 minus 1

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N. Mustikowati

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

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Pembahasan

Misalkan space straight u equals space sin space straight x  Akibatnya space du over dx equals cos space straight x space atau space dx equals fraction numerator du over denominator cos space straight x end fraction  integral subscript 0 superscript straight pi over 2 end superscript left parenthesis 2 space sin squared straight x. space cos space straight x right parenthesis space dx space  equals integral subscript 0 superscript straight pi over 2 end superscript left parenthesis 2 space straight u squared. up diagonal strike space cos space straight x end strike right parenthesis space fraction numerator du space over denominator up diagonal strike cos space straight x end strike end fraction  equals integral subscript 0 superscript straight pi over 2 end superscript 2 space straight u squared. du  equals right enclose 2 over 3 straight u cubed end enclose subscript 0 superscript straight pi over 2 end superscript  equals right enclose 2 over 3 sin cubed straight x end enclose subscript 0 superscript straight pi over 2 end superscript  equals 2 over 3 open parentheses sin cubed open parentheses straight pi over 2 close parentheses minus 0 close parentheses  equals 2 over 3

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