Pertanyaan

Nilai ∫ 6 1 π 3 1 π ( 3 cos x − 5 sin x ) d x = ...

Nilai $\int_{\frac{1}{6} π}^{\frac{1}{3} π} (3 cos x - 5 sin x) d x = ...$

O. Rahmawati

Master Teacher

Mahasiswa/Alumni UIN Sunan Gunung Djati Bandung

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah C.

Pembahasan

Ingat! Mengoperasikan integral: Oleh karena itu, jawaban yang benar adalah C.

Ingat!

integral cos space x space straight d x equals space sin space x space plus C integral space sin space x space straight d x equals negative cos space x space plus C space

Mengoperasikan integral:

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral subscript 1 over 6 straight pi end subscript superscript 1 third straight pi end superscript open parentheses 3 space cos space x space minus space 5 space sin space x close parentheses space straight d x end cell row blank equals cell open square brackets 3 space sin space x plus 5 space cos space x close square brackets subscript 1 over 6 straight pi end subscript superscript 1 third straight pi end superscript end cell row blank equals cell open square brackets 3 space sin space straight pi over 3 plus 5 space cos space straight pi over 3 close square brackets minus open square brackets 3 space sin straight pi over 6 plus 5 space cos straight pi over 6 close square brackets end cell row blank equals cell open square brackets 3 open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses plus 5 open parentheses 1 half close parentheses close square brackets minus open square brackets 3 open parentheses 1 half close parentheses plus 5 open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses close square brackets end cell row blank equals cell fraction numerator 3 square root of 3 over denominator 2 end fraction minus fraction numerator 5 square root of 3 over denominator 2 end fraction plus 5 over 2 minus 3 over 2 end cell row blank equals cell fraction numerator negative 2 square root of 3 over denominator 2 end fraction plus 2 over 2 end cell row blank equals cell negative square root of 3 plus 1 end cell row blank equals cell 1 minus square root of 3 end cell end table$

Oleh karena itu, jawaban yang benar adalah C.