Integral Trigonometri: Bentuk Perkalian

Bentuk Perkalian

$2 \sin A . \cos B = \sin (A + B) + \sin (A - B)$

$2 \cos A . \sin B = \sin (A + B) - \sin (A - B)$

$2 \cos A . \cos B = \cos (A + B) + \cos (A - B)$

$- 2 \sin A . \sin B = \cos (A + B) - \cos (A - B)$

Contoh 01

$\begin{aligned} \int 6 \sin 3 x \cos 2 x d x \\ 3 \int 2 \sin 3 x \cos 2 x d x \\ 2 \sin A \cos B = \sin (A + B) + \sin (A - B) \\ 3 \int \sin (3 x + 2 x) + \sin (3 x - 2 x) d x \\ 3 \int \sin 5 x + \sin x d x \\ 3 \int \sin 5 x \frac{d (5 x)}{5} + 3 \int \sin x d x \\ - \frac{3}{5} \cos 5 x - 3 \cos x + c \end{aligned}$

Contoh 02

$\begin{aligned} \int \sin x \sin 5 x d x \\ - \frac{1}{2} \int - 2 \sin x \sin 5 x d x \\ - 2 \sin A \sin B = \cos (A + B) - \cos (A - B) \\ - \frac{1}{2} \int \cos (x + 5 x) - \cos (x - 5 x) d x \\ - \frac{1}{2} \int \cos 6 x - \cos (- 4 x) d x \\ - \frac{1}{2} \int \cos 6 x - \cos 4 x d x \\ - \frac{1}{2} \int \cos 6 x \frac{d (6 x)}{6} + \frac{1}{2} \cos 4 x \frac{d (4 x)}{4} \\ - \frac{1}{12} \sin 6 x + \frac{1}{8} \sin 4 x + c \end{aligned}$

SOAL LATIHAN

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