Pertanyaan

Diketahui dan maka ....

Diketahui dan maka begin mathsize 14px style integral from 0 to pi over 4 of g open parentheses f open parentheses x close parentheses close parentheses times h open parentheses x close parentheses blank d x equals end style ....

$begin mathsize 14px style fraction numerator square root of 2 over denominator 15 end fraction end style$
$begin mathsize 14px style fraction numerator 2 square root of 2 over denominator 15 end fraction end style$
$begin mathsize 14px style fraction numerator 4 square root of 2 over denominator 15 end fraction end style$
$begin mathsize 14px style fraction numerator square root of 3 over denominator 12 end fraction end style$
$begin mathsize 14px style fraction numerator 4 square root of 3 over denominator 12 end fraction end style$

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Klaim

N. Rahayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

Gunakan rumus dan perbandingan trigonometri di bawah ini untuk menyederhanakan bentuk : Maka,

Gunakan rumus dan perbandingan trigonometri di bawah ini untuk menyederhanakan bentuk :

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sin squared invisible function application x plus cos squared invisible function application x end cell equals 1 row cell csc invisible function application x end cell equals cell fraction numerator 1 over denominator sin invisible function application x end fraction end cell row cell negative 2 sin invisible function application A sin invisible function application B end cell equals cell cos invisible function application open parentheses A plus B close parentheses minus cos invisible function application open parentheses A minus B close parentheses end cell end table end style$

Maka,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript 0 superscript pi over 4 end superscript g open parentheses f open parentheses x close parentheses close parentheses times h open parentheses x close parentheses blank d x blank end cell equals cell integral subscript 0 superscript pi over 4 end superscript g open parentheses sin invisible function application 4 x csc invisible function application x close parentheses open parentheses 1 minus cos squared invisible function application x close parentheses blank d x end cell row blank equals cell integral subscript 0 superscript pi over 4 end superscript 2 sin invisible function application 4 x open parentheses fraction numerator 1 over denominator sin invisible function application x end fraction close parentheses open parentheses sin squared invisible function application x close parentheses blank d x end cell row blank equals cell integral subscript 0 superscript pi over 4 end superscript 2 sin invisible function application 4 x sin invisible function application x d x end cell row blank equals cell integral subscript 0 superscript pi over 4 end superscript minus open square brackets cos invisible function application open parentheses 4 x plus x close parentheses minus cos invisible function application open parentheses 4 x minus x close parentheses close square brackets d x end cell row blank equals cell integral subscript 0 superscript pi over 4 end superscript minus cos invisible function application open parentheses 5 x close parentheses plus cos invisible function application open parentheses 3 x close parentheses d x end cell row blank equals cell negative 1 fifth sin invisible function application 5 x plus 1 third sin invisible function application 3 x end cell row blank equals cell open negative 1 fifth sin invisible function application 5 x plus 1 third sin invisible function application 3 x close square brackets subscript 0 superscript pi over 4 end superscript end cell row blank equals cell open parentheses negative 1 fifth sin invisible function application open parentheses fraction numerator 5 pi over denominator 4 end fraction close parentheses plus 1 third sin invisible function application open parentheses fraction numerator 3 pi over denominator 4 end fraction close parentheses close parentheses minus open parentheses negative 1 fifth sin invisible function application 0 plus 1 third sin invisible function application 0 close parentheses end cell row blank equals cell negative 1 fifth open parentheses negative fraction numerator square root of 2 over denominator 2 end fraction close parentheses plus 1 third open parentheses fraction numerator square root of 2 over denominator 2 end fraction close parentheses end cell row blank equals cell fraction numerator square root of 2 over denominator 10 end fraction plus fraction numerator square root of 2 over denominator 6 end fraction end cell row blank equals cell fraction numerator 16 square root of 2 over denominator 60 end fraction end cell row blank equals cell fraction numerator 4 square root of 2 over denominator 15 end fraction end cell end table end style$