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Pertanyaan

Jika , maka nilai dari 20 y ​ = ....

Jika begin mathsize 14px style y equals integral from 0 to 2020 pi of open parentheses negative tan squared invisible function application x minus sec squared invisible function application x tan squared invisible function application x plus sec to the power of 4 invisible function application x close parentheses blank d x end style, maka nilai dari ....

  1. 0

  2. -1

  3. 1

  4. 11π

  5. 101π

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N. Rahayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

Gunakan identitas trigonometri berikut ini untuk menyederhanakan persamaan di atas. Sehingga, Maka diperoleh,

Gunakan identitas trigonometri berikut ini untuk menyederhanakan persamaan di atas.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell tan squared invisible function application x plus 1 end cell equals cell sec squared invisible function application x end cell row cell tan squared invisible function application x minus sec squared invisible function application x end cell equals cell negative 1 end cell end table end style

Sehingga,

begin mathsize 14px style integral from 0 to 2020 pi of open parentheses negative tan squared invisible function application x minus sec squared invisible function application x tan squared invisible function application x plus sec to the power of 4 invisible function application x close parentheses blank d x equals integral from 0 to 2020 pi of open parentheses negative tan squared invisible function application x minus sec squared invisible function application x open parentheses tan squared invisible function application x minus sec squared invisible function application x close parentheses close parentheses blank d x equals integral from 0 to 2020 pi of open parentheses negative tan squared invisible function application x minus sec squared invisible function application x open parentheses negative 1 close parentheses close parentheses d x equals integral from 0 to 2020 pi of open parentheses negative tan squared invisible function application x plus sec squared invisible function application x close parentheses d x equals negative integral from 0 to 2020 pi of open parentheses tan squared invisible function application x minus sec squared invisible function application x close parentheses d x equals negative integral from 0 to 2020 pi of open parentheses negative 1 close parentheses d x equals integral from 0 to 2020 pi of 1 d x equals open x close square brackets subscript 0 superscript 2020 pi end superscript equals 2020 pi end style

Maka diperoleh,

begin mathsize 14px style y over 20 equals fraction numerator 2020 pi over denominator 20 end fraction equals 101 pi end style 

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