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Pertanyaan

Nilai dari ∫ 0 2 π ​ ​ ( sin 5 x − sin x ) d x = ...

Nilai dari 

  1. negative 4 over 5

  2. negative 1 fifth

  3. negative 1 half

  4. 1

  5. 4 over 5

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F. Kurnia

Master Teacher

Mahasiswa/Alumni Universitas Jember

Jawaban terverifikasi

Pembahasan

integral subscript a superscript b left parenthesis a minus b right parenthesis d x equals integral subscript a superscript b a d x minus integral subscript a superscript b b d x  integral subscript a superscript b s i n invisible function application p x d x equals left square bracket negative 1 divided by p c o s invisible function application a x right square bracket subscript a superscript b  M a k a semicolon  integral subscript 0 superscript pi divided by 2 end superscript left parenthesis s i n invisible function application 5 x minus s i n invisible function application x right parenthesis d x  equals integral subscript 0 superscript pi divided by 2 end superscript s i n invisible function application 5 x d x minus integral subscript 0 superscript pi divided by 2 end superscript s i n invisible function application x d x  equals vertical line minus 1 fifth c o s invisible function application 5 x vertical line subscript 0 superscript pi divided by 2 end superscript minus vertical line minus c o s invisible function application x vertical line subscript 0 superscript pi divided by 2 end superscript  equals open parentheses negative 1 fifth space space cos invisible function application 5 open parentheses pi over 2 close parentheses minus open parentheses negative 1 fifth space space cos invisible function application 5 left parenthesis 0 right parenthesis close parentheses close parentheses minus open parentheses negative cos invisible function application open parentheses pi over 2 close parentheses minus left parenthesis negative cos invisible function application left parenthesis 0 right parenthesis right parenthesis close parentheses  equals open parentheses 0 plus 1 fifth close parentheses minus left parenthesis 0 plus 1 right parenthesis equals 1 fifth minus 1 equals negative 4 over 5

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nilai k antara o dan π yang membuat ∫ 0 k ​ sin 2 x cos x d x maksimum adalah...

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