Hasil dari ∫(5−4x+9x2+4x3 )dx=...

Pertanyaan

$\mathrm{Hasil}\;\mathrm{dari}\;\int\left(5-4x+9x^2+4x^3\;\right)dx=...$

Y. Laksmi

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Pembahasan

$Integral space fungsi space polinom space adalah space integral a x to the power of n d x space equals space fraction numerator a over denominator n plus 1 end fraction x to the power of n plus 1 end exponent plus C Gunakan space formula space diatas space untuk space menyelesaikan space integral space dalam space soal space integral open parentheses 5 minus 4 x plus 9 x squared plus 4 x cubed close parentheses d x equals open parentheses fraction numerator 5 over denominator 0 plus 1 end fraction x to the power of 0 plus 1 end exponent close parentheses minus open parentheses fraction numerator 4 over denominator 1 plus 1 end fraction x to the power of 1 plus 1 end exponent close parentheses plus open parentheses fraction numerator 9 over denominator 2 plus 1 end fraction x to the power of 2 plus 1 end exponent close parentheses plus open parentheses fraction numerator 4 over denominator 3 plus 1 end fraction x to the power of 3 plus 1 end exponent close parentheses plus C equals 5 over 1 x to the power of 1 minus 4 over 2 x squared plus 9 over 3 x cubed plus 4 over 4 x to the power of 4 plus C equals 5 x minus 2 x squared plus 3 x cubed plus x to the power of 4 plus C equals x to the power of 4 plus 3 x cubed minus 2 x squared plus 5 x plus C$