Selesaikan integral berikut! d. ∫(6x2+2x−3)dx

Pertanyaan

Selesaikan integral berikut!

d. begin mathsize 14px style integral open parentheses 6 x squared plus 2 x minus 3 close parentheses d x end style

L. Marlina

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Jawaban

nilai begin mathsize 14px style integral open parentheses 6 x squared plus 2 x minus 3 close parentheses d x end style yaitu begin mathsize 14px style 2 x cubed plus x squared minus 3 x plus C end style.

Pembahasan

Perhatikan perhitungan berikut ini.

begin mathsize 14px style integral f open parentheses left parenthesis x right parenthesis d x plus g left parenthesis x right parenthesis close parentheses d x equals integral f left parenthesis x right parenthesis d x plus integral g left parenthesis x right parenthesis d x end style 

Maka integral begin mathsize 14px style integral open parentheses 6 x squared plus 2 x minus 3 close parentheses d x end style yaitu:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral open parentheses 6 x squared plus 2 x minus 3 close parentheses d x end cell equals cell integral 6 x squared d x plus integral 2 x d x minus integral 3 d x end cell row blank equals cell fraction numerator 6 over denominator 2 plus 1 end fraction x to the power of 2 plus 1 end exponent plus fraction numerator 2 over denominator 1 plus 1 end fraction x to the power of 1 plus 1 end exponent minus 3 x end cell row blank equals cell 6 over 3 x cubed plus 2 over 2 x squared minus 3 x end cell row blank equals cell 2 x cubed plus x squared minus 3 x plus C end cell end table end style

Dengan demikian, nilai begin mathsize 14px style integral open parentheses 6 x squared plus 2 x minus 3 close parentheses d x end style yaitu begin mathsize 14px style 2 x cubed plus x squared minus 3 x plus C end style.

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