Tentukan integral berikut ini : 7. ∫(5−x+x2−x3+x4) dx

Pertanyaan

Tentukan integral berikut ini :

7. $\style{font-size:14px}{\int\left(5-x+x^2-x^3+x^4\right)\;\operatorname dx}$

R. Nurhayati

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Pembahasan

Perhatikan penyelesaian integral berikut!

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

Jadi, kita peroleh nilai dari integral tersebut adalah sebagai berikut.