Pertanyaan

∫ 6 x 6 − x 2 dx

$\int 6 x 6 - x^{2} dx$

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H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

table attributes columnalign right center left columnspacing 0px end attributes row blank blank integral end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 6 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of 6 minus x squared end root end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank d end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 6 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 6 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

Penyelesaian integral tersebut menggunakan metode integral substitusi sebagai berikut. Misal: Dengan demikian,

Penyelesaian integral tersebut menggunakan metode integral substitusi sebagai berikut.

integral 6 x square root of 6 minus x squared end root space text dx end text

Misal: $u equals 6 minus x squared space rightwards arrow space fraction numerator d u over denominator d x end fraction equals negative 2 x space text atau end text space d x equals fraction numerator d u over denominator negative 2 x end fraction$

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral 6 x square root of 6 minus x squared end root space d x end cell equals cell integral 6 x open parentheses u close parentheses to the power of 1 half end exponent times fraction numerator d u over denominator negative 2 x end fraction end cell row blank equals cell integral negative 3 open parentheses u close parentheses to the power of 1 half end exponent space d u end cell row blank equals cell negative 3 times 2 over 3 open parentheses u close parentheses to the power of 3 over 2 end exponent plus c end cell row blank equals cell negative 2 u square root of u plus c end cell row blank equals cell negative 2 open parentheses 6 minus x squared close parentheses square root of 6 minus x squared end root plus c end cell end table$

Dengan demikian,