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Pertanyaan

Jika f left parenthesis x right parenthesis equals left square bracket 2 a x squared plus left parenthesis a plus 1 right parenthesis x right square bracket space d x comma f left parenthesis 2 right parenthesis equals 24 comma dan f left parenthesis 1 right parenthesis equals 4 comma tentukan nilai begin mathsize 14px style a end style.

I. Kumaralalita

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Pembahasan

Terdapat kesalahan pada soal. Fungsi f left parenthesis x right parenthesis yang benar dan hasil integralnya adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell integral open parentheses 2 a x squared plus open parentheses a plus 1 close parentheses x close parentheses d x end cell row cell f open parentheses x close parentheses end cell equals cell fraction numerator 2 a over denominator 3 end fraction x cubed plus fraction numerator open parentheses a plus 1 close parentheses over denominator 2 end fraction x squared plus C end cell row blank blank blank row blank blank blank end table end style 

Untuk table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses 2 close parentheses end cell equals 24 end table, diperoleh,  

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 a over denominator 3 end fraction times 2 cubed plus fraction numerator left parenthesis a plus 1 right parenthesis over denominator 2 end fraction times 2 squared plus C end cell equals 24 row cell fraction numerator 16 a over denominator 3 end fraction plus 2 open parentheses a plus 1 close parentheses plus C end cell equals 24 row cell fraction numerator 16 a over denominator 3 end fraction plus 2 a plus 2 plus C end cell equals 24 row cell 16 a plus 6 a plus 6 plus 3 C end cell equals 72 row cell 22 a plus C end cell equals cell 66 space horizontal ellipsis space asterisk times end cell end table

Untuk f open parentheses 1 close parentheses equals text 4, end text diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 2 a over denominator 3 end fraction times 1 cubed plus fraction numerator left parenthesis a plus 1 right parenthesis over denominator 2 end fraction times 1 squared plus C end cell equals 4 row cell fraction numerator 2 a over denominator 3 end fraction plus fraction numerator open parentheses a plus 1 close parentheses over denominator 2 end fraction plus C end cell equals 4 row cell 4 a plus 3 a plus 3 plus 6 C end cell equals 24 row cell 7 a plus C end cell equals cell 21 space horizontal ellipsis asterisk times asterisk times end cell end table

Persamaan * dan ** dapat dieliminasi seperti berikut

table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell table row cell 22 a plus C equals 66 end cell row cell 7 a plus C equals 21 end cell row cell 15 a equals 45 end cell row cell a equals 45 over 15 end cell row cell a equals 3 end cell end table end cell end table

Dengan demikian, nilai begin mathsize 14px style a end style adalah 3.

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