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Jika maka nilai dari adalah ....

Jika

begin mathsize 14px style f open parentheses x close parentheses equals integral subscript 0 superscript x y e to the power of y blank d y end style

maka nilai dari begin mathsize 14px style f open parentheses 1 close parentheses minus f open parentheses 1 half close parentheses end style adalah ....

  1. begin mathsize 14px style 2 square root of e end style

  2. begin mathsize 14px style square root of 2 e end root end style

  3. begin mathsize 14px style square root of e end style

  4. begin mathsize 14px style square root of e over 2 end root end style

  5. begin mathsize 14px style fraction numerator square root of e over denominator 2 end fraction end style

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L. Marlina

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

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Pembahasan

Dari soal, diketahui Kita terapkan metode integral parsial pada bentuk integral di atas. Misalkan u = y dan , maka dan Sehingga Didapat Sehingga diperoleh

Dari soal, diketahui

begin mathsize 14px style f open parentheses x close parentheses equals integral subscript 0 superscript x y e to the power of y blank d y end style

Kita terapkan metode integral parsial pada bentuk integral di atas.

Misalkan u = y dan begin mathsize 14px style fraction numerator d v over denominator d y end fraction equals e to the power of y end style, maka

begin mathsize 14px style fraction numerator d u over denominator d y end fraction equals 1 end style

dan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row v equals cell integral fraction numerator d v over denominator d y end fraction d y end cell row blank equals cell integral e to the power of y d y end cell row blank equals cell e to the power of y plus C end cell end table end style

Sehingga

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 subscript 0 superscript x y e to the power of y blank d y end cell row blank equals cell open y times e to the power of y close square brackets subscript 0 superscript x minus integral subscript 0 superscript x e to the power of y times 1 blank d x end cell row blank equals cell open parentheses x times e to the power of x minus 0 times e to the power of 0 close parentheses minus open e to the power of y close square brackets subscript 0 superscript x end cell row blank equals cell x times e to the power of x minus open parentheses e to the power of x minus e to the power of 0 close parentheses end cell row blank equals cell x e to the power of x minus e to the power of x plus 1 end cell end table end style

Didapat begin mathsize 14px style f open parentheses x close parentheses equals x e to the power of x minus e to the power of x plus 1 end style

Sehingga diperoleh

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses 1 close parentheses minus f open parentheses 1 half close parentheses end cell equals cell open parentheses 1 times e to the power of 1 minus e to the power of 1 plus 1 close parentheses minus open parentheses 1 half times e to the power of 1 half end exponent minus e to the power of 1 half end exponent plus 1 close parentheses end cell row blank equals cell e minus e plus 1 minus fraction numerator square root of e over denominator 2 end fraction plus square root of e minus 1 end cell row blank equals cell fraction numerator square root of e over denominator 2 end fraction end cell end table end style    

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