Hasil dari ∫x9−x2​dx=...

Pertanyaan

Hasil dari integral x square root of 9 minus x squared end root d x equals...

Z. Apriani

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Jawaban

hasil dari integral x square root of 9 minus x squared end root d x equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator negative 1 over denominator 3 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 9 minus x squared close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 9 minus x squared end root end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank c end table.

Pembahasan

Dengan menggunakan konsep integral, misalkan:

table attributes columnalign right center left columnspacing 0px end attributes row straight u equals cell 9 minus straight x squared end cell row du equals cell negative 2 straight x space space dx end cell row cell straight x space dx end cell equals cell negative 1 half du end cell end table

Sehingga, 

table attributes columnalign right center left columnspacing 0px end attributes row cell integral straight x square root of 9 minus straight x squared end root dx end cell equals cell integral fraction numerator negative 1 over denominator 2 end fraction square root of straight u du end cell row blank equals cell fraction numerator negative 1 over denominator 2 end fraction integral square root of straight u du end cell row blank equals cell fraction numerator negative 1 over denominator 3 end fraction straight u square root of straight u plus straight c end cell row blank equals cell fraction numerator negative 1 over denominator 3 end fraction open parentheses 9 minus straight x squared close parentheses square root of 9 minus straight x squared end root plus straight c end cell end table


Jadi, hasil dari integral x square root of 9 minus x squared end root d x equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator negative 1 over denominator 3 end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 9 minus x squared close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 9 minus x squared end root end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank c end table.

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