Pertanyaan

Nilai dari ∫ 3 ( 8 − 3 x 2 ) 2 2 x = ...

Nilai dari $\int \frac{2 x}{3 ( 8 - 3 x ^{2} ) ^{2}} = ...$

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Klaim

N. Indah

Master Teacher

Mahasiswa/Alumni Universitas Diponegoro

Jawaban terverifikasi

Jawaban

nilai dari .

nilai dari $integral fraction numerator 2 x over denominator cube root of left parenthesis 8 minus 3 x squared right parenthesis squared end root end fraction space equals space fraction numerator 2 over denominator 3 square root of 8 minus 3 x squared end root end fraction$ .

Pembahasan

Dimisalkan sehingga diperoleh: Substitusikan nilai sehingga: Dengan demikian, nilai dari .

Dimisalkan

u equals 8 minus 3 x squared

$d u equals negative 6 x space d x d x equals fraction numerator 1 over denominator negative 6 x end fraction d u$

sehingga diperoleh:

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator 2 x over denominator cube root of left parenthesis 8 minus 3 x squared right parenthesis squared end root end fraction space end cell equals cell space integral space left parenthesis 2 x right parenthesis space left parenthesis u to the power of negative 3 over 2 end exponent right parenthesis space left parenthesis fraction numerator 1 over denominator negative 6 x end fraction right parenthesis space d u end cell row blank equals cell integral space left parenthesis u to the power of negative 3 over 2 end exponent right parenthesis space left parenthesis fraction numerator 1 over denominator negative 3 end fraction right parenthesis space d u end cell row blank equals cell negative 1 third integral space left parenthesis u to the power of negative 3 over 2 end exponent right parenthesis space d u end cell row blank equals cell negative 1 third cross times fraction numerator 1 over denominator left parenthesis negative begin display style 3 over 2 end style plus 1 right parenthesis end fraction space u to the power of negative 3 over 2 plus 1 end exponent end cell row blank equals cell negative 1 third cross times fraction numerator 1 over denominator left parenthesis negative begin display style 1 half end style right parenthesis end fraction space u to the power of negative 1 half end exponent end cell row blank equals cell 2 over 3 u to the power of negative 1 half end exponent end cell row blank equals cell 2 over 3 cross times fraction numerator 1 over denominator square root of u end fraction end cell row blank equals cell fraction numerator 2 over denominator 3 square root of u end fraction end cell end table$

Substitusikan nilai u equals 8 minus 3 x squared sehingga:

$integral fraction numerator 2 x over denominator cube root of left parenthesis 8 minus 3 x squared right parenthesis squared end root end fraction space equals space fraction numerator 2 over denominator 3 square root of 8 minus 3 x squared end root end fraction$

Dengan demikian, nilai dari $integral fraction numerator 2 x over denominator cube root of left parenthesis 8 minus 3 x squared right parenthesis squared end root end fraction space equals space fraction numerator 2 over denominator 3 square root of 8 minus 3 x squared end root end fraction$ .