Pertanyaan

∫ 0 4 π cos 3 2 x . sin 2 x d x = ...

$\int_{0}^{\frac{π}{4}} cos^{3} 2 x . sin 2 x d x = ...$

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R. RGFLLIMA

Master Teacher

Jawaban terverifikasi

Pembahasan

$M i s a l space colon space u space equals space cos space 2 x comma space s u b t i t u s i k a n space b a t a s space colon x equals 0 rightwards arrow u equals cos space 2 left parenthesis 0 right parenthesis equals 1 x equals straight pi over 4 rightwards arrow cos space 2 open parentheses straight pi over 4 close parentheses equals cos space straight pi over 2 equals 0 d u equals negative 2 space sin space 2 x space d x fraction numerator d u over denominator negative 2 space sin space 2 x end fraction equals d x S e h i n g g a space b e n t u k space i n t e g r a l space m e n j a d i integral subscript 0 superscript straight pi over 4 end superscript cos cubed space 2 x. sin space 2 x space d x equals integral subscript 1 superscript 0 u cubed. up diagonal strike sin space 2 x end strike fraction numerator d u over denominator negative 2 space up diagonal strike sin space 2 x end strike end fraction equals negative 1 half integral subscript 1 superscript 0 u cubed d u equals 1 half integral subscript 0 superscript 1 u cubed d u equals 1 half. open square brackets 1 fourth u to the power of 4 close square brackets subscript 0 superscript 1 equals 1 over 8 minus 0 equals 1 over 8$