Pertanyaan

Jika untuk x ≥ 19, maka nilai ∫f(x) dx untuk x ≥ 0 adalah ….

Jika $begin mathsize 14px style integral f to the power of negative 1 end exponent open parentheses x close parentheses blank d x equals fraction numerator 2 square root of 3 over denominator 9 end fraction open parentheses x minus 19 close parentheses to the power of 3 over 2 end exponent plus C subscript 1 end style$ untuk x ≥ 19, maka nilai ∫f(x) dx untuk x ≥ 0 adalah ….

Ikuti Tryout SNBT & Menangkan E-Wallet 100rb

Habis dalam

Klaim

H. Nufus

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

Perhatikan bahwa Kemudian, jika dimisalkan , maka f(x) = y dapat dicari dengan cara sebagai berikut Maka didapat . Sehingga diperoleh

Perhatikan bahwa

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral f to the power of negative 1 end exponent open parentheses x close parentheses blank d x end cell equals cell fraction numerator 2 square root of 3 over denominator 9 end fraction open parentheses x minus 19 close parentheses to the power of 3 over 2 end exponent plus C end cell row cell fraction numerator d over denominator d x end fraction open parentheses integral f to the power of negative 1 end exponent open parentheses x close parentheses d x close parentheses end cell equals cell fraction numerator d over denominator d x end fraction open parentheses fraction numerator 2 square root of 3 over denominator 9 end fraction open parentheses x minus 19 close parentheses to the power of 3 over 2 end exponent plus C close parentheses end cell row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator 2 square root of 3 over denominator 9 end fraction times 3 over 2 times open parentheses x minus 19 close parentheses to the power of 1 half end exponent end cell row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator square root of 3 over denominator 3 end fraction open parentheses x minus 19 close parentheses to the power of 1 half end exponent end cell end table end style$

Kemudian, jika dimisalkan , maka f(x) = y dapat dicari dengan cara sebagai berikut

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f to the power of negative 1 end exponent open parentheses y close parentheses end cell equals x row cell fraction numerator square root of 3 over denominator 3 end fraction open parentheses y minus 19 close parentheses to the power of 1 half end exponent end cell equals x row cell open parentheses y minus 19 close parentheses to the power of 1 half end exponent end cell equals cell fraction numerator 3 over denominator square root of 3 end fraction x end cell row cell y minus 19 end cell equals cell open parentheses fraction numerator 3 over denominator square root of 3 end fraction x close parentheses squared end cell row cell y minus 19 end cell equals cell open parentheses fraction numerator 3 over denominator square root of 3 end fraction close parentheses squared x squared end cell row cell y minus 19 end cell equals cell 9 over 3 x squared end cell row cell y minus 19 end cell equals cell 3 x squared end cell row y equals cell 3 x squared plus 19 end cell end table end style$

Maka didapat .

Sehingga diperoleh

begin mathsize 14px style integral f left parenthesis x right parenthesis d x equals integral left parenthesis 3 x squared plus 19 right parenthesis d x equals 3 times 1 third times x cubed plus 19 x plus C equals x cubed plus 19 x plus C end style