Pertanyaan

diketahui f ( x ) = cos 2 2 x d an g ( x ) = sin 2 2 x hasil dari ∫ 0 3 2 π [ f ( x ) − g ( x ) ] d x adalah...

diketahui $f (x) = cos^{2} 2 x d an g (x) = sin^{2} 2 x$

hasil dari $\int_{0}^{\frac{2 π}{3}} [f (x) - g (x)] d x$ adalah...

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

Ingat sudut rangkap berikut ini: Jika diketahui:

Ingat sudut rangkap berikut ini:

Jika diketahui:

$f left parenthesis x right parenthesis space equals space cos squared 2 x g left parenthesis x right parenthesis space equals space sin squared 2 x m a k a colon integral subscript 0 superscript fraction numerator 2 straight pi over denominator 3 end fraction end superscript f left parenthesis x right parenthesis minus g left parenthesis x right parenthesis space d x equals integral subscript 0 superscript fraction numerator 2 straight pi over denominator 3 end fraction end superscript cos space squared space 2 x minus space sin squared space 2 x space d x equals integral subscript 0 superscript fraction numerator 2 straight pi over denominator 3 end fraction end superscript cos space 4 x space d x equals 1 fourth sin space 4 x left enclose blank with 0 below and begin inline style fraction numerator 2 straight pi over denominator 3 end fraction end style on top end enclose equals 1 fourth sin space 4 space open parentheses fraction numerator 2 straight pi over denominator 3 end fraction close parentheses plus 1 fourth sin space 4 space left parenthesis 0 right parenthesis equals 1 fourth open parentheses fraction numerator square root of 3 over denominator 2 end fraction close parentheses plus 0 equals fraction numerator square root of 3 over denominator 8 end fraction$