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Nilai dari begin mathsize 14px style integral subscript negative 1 end subscript superscript 1 open parentheses 2 x squared minus 4 x plus 3 close parentheses space d x end style adalah ...

  1. begin mathsize 14px style 22 over 3 end style 

  2. size 14px 6 

  3. begin mathsize 14px style 16 over 3 end style 

  4. begin mathsize 14px style 4 end style 

  5. begin mathsize 14px style 4 over 3 end style 

I. Kumaralalita

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Ingat!

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript a superscript b open square brackets f left parenthesis x right parenthesis plus-or-minus g left parenthesis x right parenthesis close square brackets space d x end cell equals cell integral subscript a superscript b f left parenthesis x right parenthesis space d x plus-or-minus integral subscript a superscript b g left parenthesis x right parenthesis space d x end cell row cell integral subscript a superscript b k f left parenthesis x right parenthesis space d x end cell equals cell k integral subscript a superscript b f left parenthesis x right parenthesis space d x end cell end table end style 

Sehingga dapat dihitung,

  begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral subscript negative 1 end subscript superscript 1 open parentheses 2 x squared minus 4 x plus 3 close parentheses space d x end cell row blank equals cell 2 integral subscript negative 1 end subscript superscript 1 x squared space d x minus 4 integral subscript negative 1 end subscript superscript 1 x space d x plus integral subscript negative 1 end subscript superscript 1 3 space d x end cell row blank equals cell 2 open square brackets 1 third x cubed close square brackets subscript negative 1 end subscript superscript 1 minus 4 open square brackets 1 half x squared close square brackets subscript negative 1 end subscript superscript 1 plus 3 open square brackets x close square brackets subscript negative 1 end subscript superscript 1 end cell row blank equals cell 2 over 3 open parentheses 1 cubed minus open parentheses negative 1 close parentheses cubed close parentheses minus 2 open parentheses 1 squared minus open parentheses negative 1 close parentheses squared close parentheses plus 3 open parentheses 1 minus open parentheses negative 1 close parentheses close parentheses end cell row blank equals cell 2 over 3 times 2 minus 2 times 0 plus 3 times 2 end cell row blank equals cell 4 over 3 minus 0 plus 6 end cell row blank equals cell fraction numerator 4 plus 18 over denominator 3 end fraction end cell row blank equals cell 22 over 3 end cell end table end style 

Dengan demikian, hasil dari begin mathsize 14px style integral subscript negative 1 end subscript superscript 1 open parentheses 2 x squared minus 4 x plus 3 close parentheses space d x equals 22 over 3 end style.

Jadi, jawaban yang tepat adalah A.

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