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Hasil ∫−2π​2π​​(sin3 t cos t)dt= ....

Pertanyaan

Hasil begin mathsize 14px style integral subscript negative pi over 2 end subscript superscript pi over 2 end superscript open parentheses sin cubed space t space cos space t close parentheses d t equals space.... end style 

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F. Nur

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Pembahasan

begin mathsize 14px style integral subscript negative pi over 2 end subscript superscript pi over 2 end superscript left parenthesis sin cubed space t space cos space t right parenthesis d t equals space.... end style 

Misalkan:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row u equals cell sin space t end cell row cell fraction numerator d u over denominator d t end fraction end cell equals cell cos space t end cell row cell d u end cell equals cell cos space t space d t end cell end table end style 

Sehingga, 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript negative pi over 2 end subscript superscript pi over 2 end superscript left parenthesis sin cubed space t space cos space t right parenthesis d t end cell equals cell space integral subscript negative pi over 2 end subscript superscript pi over 2 end superscript u cubed d u end cell row blank equals cell open square brackets fraction numerator u to the power of n plus 1 end exponent over denominator n plus 1 end fraction close square brackets subscript negative pi over 2 end subscript superscript pi over 2 end superscript end cell row blank equals cell open square brackets u to the power of 4 over 4 close square brackets subscript negative pi over 2 end subscript superscript pi over 2 end superscript end cell row blank equals cell open square brackets fraction numerator sin to the power of 4 t over denominator 4 end fraction close square brackets subscript negative pi over 2 end subscript superscript pi over 2 end superscript end cell row blank equals cell fraction numerator sin to the power of 4 open parentheses pi over 2 close parentheses over denominator 4 end fraction minus fraction numerator sin to the power of 4 open parentheses negative pi over 2 close parentheses over denominator 4 end fraction end cell row blank equals cell 1 fourth minus 1 fourth end cell row blank equals 0 end table end style

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