Pertanyaan

Untuk 0 ≤ x ≤ π . Jika f ( x ) = ∫ ( tan x sin x − 2 cos x 1 ) d x , maka f(x) naik pada interval...

Untuk $0 \leq x \leq π$ . Jika $f (x) = \int (tan x sin x - \frac{1}{2 cos x}) d x$ , maka f(x) naik pada interval...

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N. Indah

Master Teacher

Mahasiswa/Alumni Universitas Diponegoro

Jawaban terverifikasi

Pembahasan

Perhatikan bahwa f(x) naik jika f(x) > 0 Kemudian karena maka maka Sehingga daerah hasil harus memenuhi Kasus - 1 didapat daerah irisan adalah Kasus - 2 didapat daerah irisan adalah

Perhatikan bahwa f(x) naik jika f(x) > 0

Kemudian karena $begin mathsize 12px style f open parentheses x close parentheses equals integral open parentheses tan space x space sin space x minus fraction numerator 1 over denominator 2 space cos space x end fraction close parentheses d x end style$ maka $begin mathsize 12px style f apostrophe open parentheses x close parentheses equals tan space x space sin space x minus fraction numerator 1 over denominator 2 space cos space x apostrophe end fraction end style$ maka

$size 12px tan size 12px space size 12px x size 12px space size 12px sin size 12px space size 12px x size 12px minus fraction numerator size 12px 1 over denominator size 12px 2 size 12px space size 12px cos size 12px space size 12px x end fraction size 12px greater than size 12px 0 fraction numerator size 12px sin size 12px space size 12px x over denominator size 12px cos size 12px space size 12px x end fraction open parentheses size 12px sin size 12px space size 12px x close parentheses size 12px minus fraction numerator size 12px 1 over denominator size 12px 2 size 12px space size 12px cos size 12px space size 12px x end fraction size 12px greater than size 12px 0 fraction numerator size 12px sin to the power of size 12px 2 size 12px space size 12px x over denominator size 12px cos size 12px space size 12px x end fraction size 12px minus fraction numerator size 12px 1 over denominator size 12px 2 size 12px space size 12px cos size 12px space size 12px x end fraction size 12px greater than size 12px 0 fraction numerator size 12px sin to the power of size 12px 2 size 12px space size 12px x over denominator size 12px cos size 12px space size 12px x end fraction size 12px minus fraction numerator size 12px 1 over denominator size 12px 2 size 12px space size 12px cos size 12px space size 12px x end fraction size 12px greater than size 12px 0 fraction numerator size 12px 2 size 12px space size 12px sin to the power of size 12px 2 size 12px space size 12px x over denominator size 12px 2 size 12px space size 12px cos size 12px space size 12px x end fraction size 12px minus fraction numerator size 12px 1 over denominator size 12px 2 size 12px space size 12px cos size 12px space size 12px x end fraction size 12px greater than size 12px 0 fraction numerator size 12px 2 size 12px space size 12px sin to the power of size 12px 2 size 12px space size 12px x size 12px minus size 12px 1 over denominator size 12px 2 size 12px space size 12px cos size 12px space size 12px x end fraction size 12px greater than size 12px 0 fraction numerator size 12px minus size 12px space size 12px cos size 12px space size 12px 2 size 12px x over denominator size 12px 2 size 12px space size 12px cos size 12px space size 12px x end fraction size 12px greater than size 12px 0 fraction numerator size 12px cos size 12px space size 12px 2 size 12px x over denominator size 12px 2 size 12px space size 12px cos size 12px space size 12px x end fraction size 12px less than size 12px 0$

Sehingga daerah hasil harus memenuhi

Kasus - 1

didapat daerah irisan adalah

Kasus - 2

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didapat daerah irisan adalah $begin mathsize 12px style straight pi over 4 less than x less than fraction numerator begin display style straight pi end style over denominator begin display style 2 end style end fraction end style$