Pertanyaan

Hasil dari ∫ ( 4 x − 3 ) 4 d x = ...

Hasil dari $\int (4 x - 3)^{4} d x =$ ...

S. Amamah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

Gunakan integralsubstitusi, misalkan maka: Sehingga diperoleh Oleh karena jawaban yang benar adalah E.

begin mathsize 14px style integral open parentheses 4 x minus 3 close parentheses to the power of 4 space straight d x equals end style

Gunakan integral substitusi, misalkan begin mathsize 14px style u equals 4 x minus 3 end style maka:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row u equals cell 4 x minus 3 end cell row cell fraction numerator straight d u over denominator straight d x end fraction end cell equals 4 row cell straight d x end cell equals cell 1 fourth straight d u end cell row blank blank blank end table end style$

Sehingga diperoleh begin mathsize 14px style integral open parentheses 4 x minus 3 close parentheses to the power of 4 space straight d x equals end style

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral open parentheses 4 x minus 3 close parentheses to the power of 4 straight d x end cell equals cell integral u to the power of 4 space straight d x end cell row blank equals cell integral u to the power of 4 space 1 fourth space straight d u end cell row blank equals cell 1 fourth integral u to the power of 4 space straight d u end cell row blank equals cell 1 fourth open square brackets fraction numerator 1 over denominator 4 plus 1 end fraction u to the power of 4 plus 1 end exponent plus C close square brackets end cell row blank equals cell 1 fourth open square brackets 1 fifth u to the power of 5 plus C close square brackets end cell row blank equals cell 1 over 20 u to the power of 5 plus C end cell row blank equals cell 1 over 20 open parentheses 4 x minus 3 close parentheses to the power of 5 plus C end cell end table end style$

Oleh karena jawaban yang benar adalah E.