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Diketahui . Nilai dari  adalah ...

Pertanyaan

Diketahui integral subscript a minus 1 end subscript superscript 1 minus a end superscript left parenthesis x minus 1 right parenthesis space d x equals a minus 4. Nilai dari fraction numerator straight a minus 1 over denominator straight a plus 1 end fraction adalah ...

  1. 4 

  2. 3 

  3. 2 

  4. negative 2 

  5. negative 3 

Pembahasan Soal:

Diketahui :integral subscript a minus 1 end subscript superscript 1 minus a end superscript left parenthesis x minus 1 right parenthesis space d x equals a minus 4.

Ditanya : nilai dari fraction numerator straight a minus 1 over denominator straight a plus 1 end fraction ?

Jawab :
Dengan menggunakan rumus integral tentu dengan batas open square brackets straight b comma straight a close square brackets.

table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript a minus 1 end subscript superscript 1 minus a end superscript left parenthesis x minus 1 right parenthesis space d x end cell equals cell a minus 4 end cell row blank blank cell 1 half x to the power of 1 plus 1 end exponent minus x open curly brackets table attributes columnalign left end attributes row cell 1 minus a end cell row cell a minus 1 end cell end table equals a close minus 4 end cell row cell open parentheses 1 half open parentheses 1 minus a close parentheses squared minus open parentheses 1 minus a close parentheses close parentheses minus open parentheses 1 half open parentheses a minus 1 close parentheses squared minus open parentheses a minus 1 close parentheses close parentheses end cell equals cell a minus 4 end cell row cell open parentheses 1 half open parentheses 1 minus 2 a plus a squared close parentheses minus 1 plus a close parentheses minus open parentheses 1 half open parentheses a squared minus 2 a plus 1 close parentheses minus a plus 1 close parentheses end cell equals cell a minus 4 end cell row cell open parentheses 1 half minus a plus 1 half a squared minus 1 plus a close parentheses minus open parentheses 1 half a squared minus a plus 1 half minus a plus 1 close parentheses end cell equals cell a minus 4 end cell row cell 1 half minus 1 half minus a plus a plus 1 half a squared minus 1 half a squared minus 1 minus 1 plus a plus a end cell equals cell a minus 4 end cell row cell negative 2 plus 2 a end cell equals cell a minus 4 end cell row cell 2 a minus a end cell equals cell negative 4 plus 2 end cell row a equals cell negative 2 end cell end table

Subtitusi nilai a ke fraction numerator straight a minus 1 over denominator straight a plus 1 end fraction.

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator straight a minus 1 over denominator straight a plus 1 end fraction end cell equals cell fraction numerator negative 2 minus 1 over denominator negative 2 plus 1 end fraction end cell row blank equals cell fraction numerator negative 3 over denominator negative 1 end fraction end cell row blank equals 3 end table

Dengan demikian, nilai dari fraction numerator straight a minus 1 over denominator straight a plus 1 end fraction adalah 3.

Oleh karena itu, jawaban yang benar adalah B.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 10 Juni 2021

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