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Nilai dari dengan adalah ....

Nilai dari begin mathsize 14px style integral f open parentheses x close parentheses d x end style dengan begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 1 over denominator 1 plus cos invisible function application 4 x end fraction minus fraction numerator 1 over denominator 1 minus cos invisible function application 4 x end fraction end style adalah ....

  1. begin mathsize 14px style negative 1 half csc invisible function application 2 x plus C end style 

  2. size 14px 1 over size 14px 4 size 14px csc size 14px invisible function application size 14px 4 size 14px x size 14px plus size 14px C 

  3. size 14px minus size 14px 1 over size 14px 4 size 14px csc size 14px invisible function application size 14px 4 size 14px x size 14px plus size 14px C 

  4. size 14px 1 over size 14px 2 size 14px csc size 14px invisible function application size 14px 4 size 14px x size 14px plus size 14px C 

  5. size 14px minus size 14px 1 over size 14px 2 size 14px csc size 14px invisible function application size 14px 4 size 14px x size 14px plus size 14px C 

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N. Rahayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

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Perhatikan bahwa Sehingga Karena , maka

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begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 1 over denominator 1 plus cos invisible function application 4 x end fraction minus fraction numerator 1 over denominator 1 minus cos invisible function application 4 x end fraction f open parentheses x close parentheses equals fraction numerator open parentheses 1 minus cos invisible function application 4 x close parentheses minus open parentheses 1 plus cos invisible function application 4 x close parentheses over denominator open parentheses 1 plus cos invisible function application 4 x close parentheses open parentheses 1 minus cos invisible function application 4 x close parentheses end fraction f open parentheses x close parentheses equals fraction numerator negative 2 cos invisible function application 4 x over denominator 1 minus cos squared invisible function application 4 x end fraction f open parentheses x close parentheses equals fraction numerator negative 2 cos invisible function application 4 x over denominator sin squared invisible function application 4 x end fraction f open parentheses x close parentheses equals negative 2 times fraction numerator cos invisible function application 4 x over denominator sin invisible function application 4 x end fraction times fraction numerator 1 over denominator sin invisible function application 4 x end fraction f open parentheses x close parentheses equals negative 2 times cot invisible function application 4 x times csc invisible function application 4 x end style

Sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral f open parentheses x close parentheses d x end cell equals cell integral negative 2 cot invisible function application 4 x csc invisible function application 4 x d x end cell row blank equals cell negative 2 integral cot invisible function application 4 x csc invisible function application 4 x d x end cell end table end style

Karena begin mathsize 14px style integral cot invisible function application m x csc invisible function application m x d x equals negative 1 over m csc invisible function application m x plus C end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral f open parentheses x close parentheses d x end cell equals cell negative 2 integral cot invisible function application 4 x csc invisible function application 4 x d x end cell row blank equals cell negative 2 open parentheses negative 1 fourth csc invisible function application 4 x close parentheses plus C end cell row blank equals cell 1 half csc invisible function application 4 x plus C end cell end table end style 

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begin mathsize 14px style integral open parentheses sin invisible function application 4 x minus cos invisible function application 8 x close parentheses d x equals horizontal ellipsis end style 

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