Pertanyaan

∫ sin 4 x cos 4 x d x adalah ...

$\int sin^{4} x cos^{4} x d x$ adalah ...

$fraction numerator 3 x over denominator 128 end fraction space minus space 1 over 64 space sin space 2 x space plus space 1 over 256 space sin space 4 x space plus space C$
$fraction numerator 3 x over denominator 128 end fraction space plus space 1 over 64 space sin space 2 x space plus space 1 over 256 space sin space 4 x space plus space C$
$fraction numerator 3 x over denominator 64 end fraction space minus space 1 over 128 space sin space 4 x space plus space 1 over 512 space cos space 4 x space plus C$
$fraction numerator 3 x over denominator 128 end fraction space minus space 32 space sin space 4 x space plus space 124 space sin space 8 x space plus space C$
$fraction numerator 3 x over denominator 128 end fraction space minus space 1 over 128 space sin space 4 x space plus space 1 over 1024 space sin space 8 x space plus space C$

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Karenakedua pangkatnya bilangan genap, untuk menentukan penyelesaiannya gunakan: Kesamaan setengah sudut dan Sehingga Jadi, jawaban yang tepat adalah E.

Karena kedua pangkatnya bilangan genap, untuk menentukan penyelesaiannya gunakan:

Kesamaan setengah sudut $sin squared space x space equals space fraction numerator 1 space cos space 2 x over denominator 2 end fraction$ dan $cos squared space x space equals space fraction numerator 1 space plus space cos space 2 x over denominator 2 end fraction$

Sehingga

$integral space sin to the power of 4 space x space cos to the power of 4 space x space d x space equals space integral open parentheses sin squared space x close parentheses squared open parentheses cos squared space x close parentheses squared space d x equals space integral space open parentheses fraction numerator 1 space minus space cos space 2 x over denominator 2 end fraction close parentheses squared open parentheses fraction numerator 1 space plus space cos space 2 x over denominator 2 end fraction close parentheses squared space d x equals space 1 over 16 integral open parentheses 1 space minus space 2 space cos space 2 x space plus space cos squared space 2 x close parentheses open parentheses 1 space plus space 2 space cos space 2 x space plus cos squared space 2 x close parentheses space d x equals space 1 over 16 integral space open parentheses 1 space minus space 2 space cos squared space 2 x space plus space cos to the power of 4 space 2 x close parentheses space d x equals space 1 over 16 integral space d x space minus space 1 over 8 integral space cos squared space 2 x space d x space plus space 1 over 16 integral cos to the power of 4 space 2 x space d x equals 1 over 16 integral space d x space minus space 1 over 8 integral space fraction numerator 1 space plus space cos space 4 x over denominator 2 end fraction space plus space 1 over 64 integral open parentheses 1 space plus space 2 space cos space 4 x space plus space cos squared space 4 x close parentheses squared space d x equals 1 over 16 integral space d x space minus space 1 over 8 integral fraction numerator 1 space plus space cos space 4 x over denominator 2 end fraction space plus space 1 over 64 integral space d x space plus 1 over 32 integral space cos space 4 x space d x space plus space 1 over 64 integral space open parentheses fraction numerator 1 space plus space cos space 8 x over denominator 2 end fraction close parentheses space d x equals 1 over 16 integral space d x space minus space 1 over 8 integral space fraction numerator 1 space plus space cos space 4 x over denominator 2 end fraction space plus space 1 over 64 integral space d x space plus 1 over 32 integral space cos space 4 x space d x space plus space 1 over 128 integral space d x space plus space 1 over 128 integral space cos space 8 x space d x equals space 1 over 16 integral space d x space minus space 1 over 16 integral space d x space minus space 1 over 16 integral space cos space 4 x space d x space plus space 1 over 64 integral space d x space plus space 1 over 32 integral space cos space 4 x space d x space plus space 1 over 128 integral space d x space plus space integral space 1 over 128 space cos space 8 x space d x equals space 3 over 128 integral space d x space minus space 1 over 32 integral space cos space 4 x space d x space plus space 1 over 128 integral space cos space 8 x space d x equals space fraction numerator 3 x over denominator 128 end fraction minus 1 over 128 space sin space 4 x space plus space 1 over 1024 space sin space 8 x space plus space C$

Jadi, jawaban yang tepat adalah E.