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Hasil dari ∫2x−5​4​dx adalah...

Pertanyaan

Hasil dari integral fraction numerator 4 over denominator square root of 2 x minus 5 end root end fraction straight d x adalah...

  1. 1 fourth square root of 2 x minus 5 end root plus straight C space

  2. 1 half square root of 2 x minus 5 end root plus straight C 

  3. square root of 2 x minus 5 end root plus straight C 

  4. 2 square root of 2 x minus 5 end root plus straight C 

  5. 4 square root of 2 x minus 5 end root plus straight C 

K. Putri

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Ganesha

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Soal di atas dapat diselesaikan dengan metode substitusi. Terlebih dahulu, misalkan:

table attributes columnalign right center left columnspacing 0px end attributes row u equals cell 2 x minus 5 end cell row blank rightwards double arrow cell fraction numerator d u over denominator d x end fraction equals 2 end cell row blank rightwards double arrow cell straight d u equals 2 space straight d x end cell end table 

Kemudian substitusi nilai di atas ke soal integral berikut:

table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator 4 over denominator square root of 2 x minus 5 end root end fraction straight d x end cell equals cell integral fraction numerator 2 over denominator square root of u end fraction d u end cell row blank equals cell integral 2 u to the power of negative 1 half end exponent straight d u end cell row blank equals cell 2 integral u to the power of negative 1 half end exponent straight d u end cell row blank equals cell 2 times 2 u to the power of 1 half end exponent plus straight C end cell row blank equals cell 4 u to the power of 1 half end exponent plus straight C end cell row blank equals cell 4 u to the power of 1 half end exponent plus straight C end cell row blank equals cell 4 open parentheses 2 x minus 5 close parentheses to the power of 1 half end exponent plus straight C end cell row blank equals cell 4 square root of 2 x minus 5 end root plus straight C end cell end table

Oleh karena itu, jawaban yang benar adalah D.

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