Hasil dari  adalah ....

Pertanyaan

Hasil dari begin mathsize 14px style integral open parentheses fraction numerator cot x minus sec squared x over denominator ccs x end fraction close parentheses space straight d x end style adalah ....

  1. begin mathsize 14px style sin invisible function application x minus sec invisible function application x plus C end style

  2. begin mathsize 14px style scs invisible function application x plus tan invisible function application x plus C end style

  3. begin mathsize 14px style cos invisible function application x minus sin invisible function application x plus C end style

  4. begin mathsize 14px style sin invisible function application x plus sec invisible function application x plus C end style

  5. begin mathsize 14px style tan invisible function application x plus x plus C end style

D. Natalia

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D. 

Pembahasan

Ingat kembali perbandingan trigonometri berikut!

begin mathsize 14px style cot invisible function application x equals fraction numerator cos invisible function application x over denominator sin invisible function application x end fraction tan invisible function application x equals fraction numerator sin invisible function application x over denominator cos invisible function application x end fraction csc invisible function application x equals fraction numerator 1 over denominator sin invisible function application x end fraction end style

Oleh karena itu, diperoleh hasil perhitungan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral open parentheses fraction numerator cot x minus sec squared x over denominator ccs x end fraction close parentheses space straight d x end cell row blank equals cell integral open parentheses fraction numerator fraction numerator cos x over denominator sin x end fraction minus fraction numerator 1 over denominator cos squared x end fraction over denominator fraction numerator 1 over denominator sin x end fraction end fraction close parentheses space straight d x end cell row blank equals cell integral open parentheses fraction numerator cos cubed x minus sin x over denominator sin x cos squared x end fraction times fraction numerator sin x over denominator 1 end fraction close parentheses space straight d x end cell row blank equals cell integral open parentheses fraction numerator cos cubed x minus sin x over denominator cos squared x end fraction close parentheses space straight d x end cell row blank equals cell integral open parentheses cos x minus sec x tan x close parentheses space straight d x end cell row blank equals cell integral cos x space straight d x plus integral sec x tan x space straight d x end cell row blank equals cell sin x plus sec x plus C end cell end table end style

Jadi, jawaban yang tepat adalah D. 

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