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Pertanyaan

Hasil dari ∫ 1 − x 2 ​ d x = ....

Hasil dari ....

  1. begin mathsize 14px style 1 half open parentheses square root of 1 minus x squared end root plus a r c cos invisible function application x close parentheses plus C end style 

  2. begin mathsize 14px style 1 fourth open parentheses x square root of 1 minus x squared end root plus a r c sin invisible function application x close parentheses plus C end style 

  3. begin mathsize 14px style 1 half open parentheses square root of 1 minus x squared end root plus a r c tan invisible function application x close parentheses plus C end style 

  4. begin mathsize 14px style 1 half open parentheses x square root of 1 minus x squared end root plus a r c tan invisible function application x close parentheses plus C end style 

  5. begin mathsize 14px style 1 half open parentheses x square root of 1 minus x squared end root plus a r c sin invisible function application x close parentheses plus C end style 

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N. Rahayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

Misalkan: x = sin⁡θ ⟺ θ = arc sin⁡x dx = cos⁡θ dθ Kemudian karena sin⁡θ = x maka diperoleh, Sehingga,

Misalkan:
x = sin⁡θ ⟺ θ = arc sin⁡x
dx = cos⁡θ dθ

Kemudian karena sin⁡θ = x maka diperoleh,

begin mathsize 14px style cos invisible function application theta equals square root of 1 minus x squared end root end style

Sehingga,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral square root of 1 minus x squared end root blank d x end cell equals cell integral square root of 1 minus sin squared invisible function application theta end root blank open parentheses cos invisible function application theta blank d theta close parentheses end cell row blank equals cell integral square root of cos squared invisible function application theta end root blank open parentheses cos invisible function application theta blank d theta close parentheses end cell row blank equals cell integral cos squared invisible function application theta d theta end cell row blank equals cell integral 1 half open parentheses cos invisible function application 2 theta plus 1 close parentheses d theta end cell row blank equals cell 1 half open parentheses 1 half sin invisible function application 2 theta plus theta close parentheses plus C end cell row blank equals cell 1 half open parentheses 1 half sin invisible function application 2 theta plus theta close parentheses plus C end cell row blank equals cell 1 half open parentheses 1 half times 2 sin invisible function application theta cos invisible function application theta plus theta close parentheses plus C end cell row blank equals cell 1 half open parentheses x square root of 1 minus x squared end root plus a r c sin invisible function application x close parentheses plus C end cell end table end style 

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