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Diketahui F ( x ) = 6 x 2 − 2 x + 1 dan untuk x = 2 , F ( x ) bernilai 4. Tentukan fungsi .

Diketahui  dan untuk ,  bernilai 4. Tentukan fungsi begin mathsize 14px style straight F left parenthesis straight x right parenthesis end style.

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fungsi

fungsi begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight F left parenthesis straight x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank cubed end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank squared end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table 10 end style  

Pembahasan

Diketahui: dan untuk , bernilai 4. Ditanya: Tentukan fungsi . Jawaban: Dengan menerapkan konsep integral sebagai anti turunan, maka Maka: Kesimpulan: Jadi, fungsi

Diketahui:

begin mathsize 14px style straight F apostrophe left parenthesis straight x right parenthesis equals 6 straight x squared minus 2 straight x plus 1 end style dan untuk begin mathsize 14px style x equals 2 end style, begin mathsize 14px style straight F left parenthesis straight x right parenthesis end style bernilai 4.

Ditanya:

Tentukan fungsi begin mathsize 14px style straight F left parenthesis straight x right parenthesis end style.

Jawaban:

Dengan menerapkan konsep integral sebagai anti turunan, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight F left parenthesis straight x right parenthesis end cell equals cell integral straight F apostrophe left parenthesis straight x right parenthesis end cell row blank equals cell integral left parenthesis 6 straight x squared minus 2 straight x plus 1 right parenthesis dx end cell row blank equals cell 6 over 3 straight x cubed minus 2 over 2 straight x squared plus straight x plus straight c end cell row blank equals cell 2 straight x cubed minus straight x squared plus straight x plus straight c end cell end table end style  

Maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight F left parenthesis x right parenthesis end cell equals cell 2 left parenthesis x right parenthesis cubed minus left parenthesis x right parenthesis squared plus x plus straight c end cell row cell straight F left parenthesis 2 right parenthesis end cell equals cell 2 left parenthesis 2 right parenthesis cubed minus left parenthesis 2 right parenthesis squared plus 2 plus straight c end cell row 4 equals cell 2 times 8 minus 4 plus 2 plus straight c end cell row 4 equals cell 16 minus 2 plus straight c end cell row cell 4 minus 14 end cell equals straight c row cell negative 10 end cell equals straight c end table end style  

Kesimpulan:

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight F left parenthesis straight x right parenthesis end cell equals cell 2 straight x cubed minus straight x squared plus straight x plus straight c end cell row blank equals cell 2 straight x cubed minus straight x squared plus straight x minus 10 end cell end table end style  

Jadi, fungsi begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight F left parenthesis straight x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank cubed end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank squared end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table 10 end style  

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