Pertanyaan

Luas daerah yang dibatasi oleh kurva y = x 2 − 6 x + 5 dan sumbu X adalah ...

Luas daerah yang dibatasi oleh kurva $y = x^{2} - 6 x + 5$ dan sumbu $X$ adalah ...

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Untuk mencari luas daerah, gunakan integral : Berlaku aturan: Kemudian cari faktor dari , Subtitusikan ke hasil integral, Oleh karena itu, jawaban yang benar adalah C.

Untuk mencari luas daerah, gunakan integral :

integral x squared minus 6 x plus 5

Berlaku aturan:

$integral x to the power of n d x equals fraction numerator x to the power of n plus 1 end exponent over denominator n plus 1 end fraction$

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral x squared minus 6 x plus 5 end cell equals cell integral x squared d x minus 6 integral x d x plus integral 1 d x end cell row blank blank blank row n equals 2 row cell integral x squared end cell equals cell fraction numerator x to the power of 2 plus 1 end exponent over denominator 2 plus 1 end fraction end cell row blank equals cell x cubed over 3 end cell row blank blank blank row n equals 1 row cell integral x space d x end cell equals cell fraction numerator x to the power of 1 plus 1 end exponent over denominator 1 plus 1 end fraction end cell row blank equals cell x squared over 2 end cell row blank blank blank row n equals 0 row cell integral 1 d x end cell equals cell fraction numerator x to the power of 0 plus 1 end exponent over denominator 0 plus 1 end fraction end cell row blank equals cell x to the power of 1 over 1 end cell row blank equals x row blank blank blank row blank blank cell integral x squared d x minus 6 integral x d x plus integral 1 d x end cell row blank equals cell x cubed over 3 minus 6 open parentheses x squared over 2 close parentheses plus 5 left parenthesis x right parenthesis plus C end cell row blank equals cell x cubed over 3 minus open parentheses fraction numerator 6 x squared over denominator 2 end fraction close parentheses plus 5 x plus C end cell row blank equals cell x cubed over 3 minus 3 x squared plus 5 x plus C end cell end table$

Kemudian cari faktor dari y equals x squared minus 6 x plus 5 ,

table attributes columnalign right center left columnspacing 0px end attributes row cell x squared minus 6 x plus 5 end cell equals cell open parentheses x minus 5 close parentheses open parentheses x minus 1 close parentheses end cell row cell x minus 5 end cell equals 0 row x equals 5 row cell x minus 1 end cell equals 0 row x equals 1 end table

Subtitusikan ke hasil integral,

$table attributes columnalign right center left columnspacing 0px end attributes row straight x equals cell 5 space dikurangi space straight x equals 1 end cell row blank blank cell open parentheses 5 cubed over 3 minus 3 left parenthesis 5 right parenthesis squared plus 5 left parenthesis 5 right parenthesis close parentheses minus open parentheses 1 cubed over 3 minus 3 left parenthesis 1 right parenthesis squared plus 5 left parenthesis 1 right parenthesis close parentheses end cell row blank equals cell open parentheses 125 over 3 minus 3 left parenthesis 25 right parenthesis plus 25 close parentheses minus open parentheses 1 third minus 3 plus 5 close parentheses end cell row blank equals cell open parentheses 125 over 3 minus 75 plus 25 close parentheses minus open parentheses 1 third plus 2 close parentheses end cell row blank equals cell open parentheses 125 over 3 minus 50 close parentheses minus open parentheses fraction numerator 1 minus 6 over denominator 3 end fraction close parentheses end cell row blank equals cell open parentheses fraction numerator 125 minus 150 over denominator 3 end fraction close parentheses minus open parentheses fraction numerator 1 minus 6 over denominator 3 end fraction close parentheses end cell row blank equals cell fraction numerator negative 25 over denominator 3 end fraction minus 7 over 3 end cell row blank equals cell negative 32 over 3 end cell end table$

Oleh karena itu, jawaban yang benar adalah C.