Pertanyaan

Tentukan integral berikut ini. ∫ ( 100 x 4 − 60 x 3 + 30 x 2 − 10 x + 1 ) d x

Tentukan integral berikut ini.

$\int (100 x^{4} - 60 x^{3} + 30 x^{2} - 10 x + 1) d x$

R. Nurhayati

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Pembahasan

Perhatikan penyelesaian integral berikut! Jadi, nilai dari integral fungsi tersebut adalah sebagai berikut.

Perhatikan penyelesaian integral berikut!

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral left parenthesis 100 x to the power of 4 minus 60 x cubed plus 30 x squared minus 10 x plus 1 right parenthesis space d x end cell row blank equals cell 100 integral x to the power of 4 d x minus 60 integral x cubed d x plus 30 integral x squared d x minus 10 integral x d x plus integral 1 d x end cell row blank equals cell fraction numerator 100 over denominator 4 plus 1 end fraction x to the power of 4 plus 1 end exponent minus fraction numerator 60 over denominator 3 plus 1 end fraction x to the power of 3 plus 1 end exponent plus fraction numerator 30 over denominator 2 plus 1 end fraction x to the power of 2 plus 1 end exponent minus fraction numerator 10 over denominator 1 plus 1 end fraction x to the power of 1 plus 1 end exponent plus x plus C end cell row blank equals cell 100 over 5 x to the power of 5 minus 60 over 4 x to the power of 4 plus 30 over 3 x cubed minus 10 over 2 x squared plus x plus C end cell row blank equals cell 20 x to the power of 5 minus 15 x to the power of 4 plus 10 x cubed minus 5 x squared plus x plus C end cell end table end style$

Jadi, nilai dari integral fungsi tersebut adalah sebagai berikut.