Pertanyaan

Jika periode fungsi f ( x ) = 2 cos ( a x ) + a adalah 3 π , maka nilai minimum fungsi ∫ adalah....

Jika periode fungsi $f (x) = 2 cos (a x) + a$ adalah $\frac{π}{3}$ , maka nilai minimum fungsi $\int$ adalah....

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A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

$i right parenthesis N i l a i space m a k s i m u m space d a n space m i n i m u m space p a d a space f u n g s i space t r i g o n o m e t r i f left parenthesis x right parenthesis equals cos space invisible function application x rightwards arrow negative 1 less or equal than f left parenthesis x right parenthesis less or equal than 1 space f left parenthesis x right parenthesis equals cos space invisible function application a x rightwards arrow negative 1 less or equal than f left parenthesis x right parenthesis less or equal than 1 space f left parenthesis x right parenthesis equals 2 space cos invisible function application a x rightwards arrow negative 2 less or equal than f left parenthesis x right parenthesis less or equal than 2 f open parentheses x close parentheses equals 2 cos invisible function application a x plus a rightwards arrow negative 2 plus a less or equal than f open parentheses x close parentheses less or equal than 2 plus a i i right parenthesis P e r i o d e space p a d a space f u n g s i space t r i g o n o m e t r i F u n g s i space f left parenthesis x right parenthesis equals a space cos invisible function application b x plus c space m e m i l i k i space p e r i o d e space fraction numerator 2 pi over denominator open vertical bar b close vertical bar end fraction S e h i n g g a space f u n g s i space f left parenthesis x right parenthesis equals 2 space cos invisible function application left parenthesis a x right parenthesis plus a space m e m i l i k i space p e r i o d e space fraction numerator 2 pi over denominator open vertical bar a close vertical bar end fraction i i i right parenthesis B a n d i n g k a n space p e r i o d e space f u n g s i space D a r i space p e r h i t u n g a n space d i d a p a t space p e r i o d e space fraction numerator 2 pi over denominator open vertical bar a close vertical bar end fraction D a r i space s o a l space d i d a p a t space p e r i o d e space pi over 3 M a k a fraction numerator 2 pi over denominator open vertical bar a close vertical bar end fraction equals pi over 3 vertical line a vertical line equals 6 space a equals plus-or-minus 6 i v right parenthesis H i t u n g space n i l a i space m i n i m u m space f u n g s i space D a r i space s e b e l u m n y a space d i d a p a t space n i l a i space m i n i m u m space f u n g s i space a d a l a h space minus 2 plus a. space space U n t u k space a equals negative 6 rightwards arrow m i n invisible function application f left parenthesis x right parenthesis equals negative 2 plus left parenthesis negative 6 right parenthesis equals negative 8 space U n t u k space a equals 6 rightwards arrow m i n invisible function application f left parenthesis x right parenthesis equals negative 2 plus 6 equals 4$