Pertanyaan

Hasil ∫ − 2 π 2 π ( sin 3 t cos t ) d t = ....

Hasil $\int_{- \frac{π}{2}}^{\frac{π}{2}} (sin^{3} t cos t) d t = ....$

F. Nur

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Pembahasan

Misalkan: Sehingga,

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,

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