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Pilihlah seluruh fungsi $f$ yang memenuhi syarat Teorema Nilai Rata-rata untuk Integral pada selang $[0,1]$.

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Misal $D$ adalah daerah pada kuadran I yang dibatasi oleh grafik $y=\\var{a}x-x^2$, sumbu-$x$, garis $x=a>1$, dan garis $x=1$.

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Luas daerah $D$ bernilai maksimum saat $a = \\ldots$.

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Misal $D$ adalah daerah yang dibatasi oleh grafik $y=\\var{a}x-x^2$ dan $y=x^2-\\var{a}x$. Integral yang menyatakan volume yang terbentuk jika daerah $D$ diputar terhadap garis $x=\\var{a+1}$ adalah $\\ldots$.

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Suatu racun yang ringan dikenalkan ke dalam koloni bakteri dengan populasinya $600000$. Diperoleh hasil pengamatannya adalah $R(t)=200e^{0.01t}$ bakteri per jam lahir pada koloni saat waktu $t$ jam dan fraksi populasi yang bertahan hidup saat waktu $t$ jam adalah $S(t) = e^{-0.015t}$.

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Tentukan populasi koloni setelah $10$ jam.

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Petunjuk: Bulatkan jawaban Anda ke bilangan asli terdekat.

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Misal $D$ adalah daerah yang dibatasi oleh grafik $y=\\cos(x)$ dan $y=\\sin(2x)$ pada selang $\\left[ 0,\\dfrac{\\pi}{2} \\right]$.

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Tentukan volume benda pejal dengan alas $D$ jika penampang yang tegak lurus dengan sumbu-$x$ selalu berbentuk segitiga sama kaki dengan tinggi $\\var{a}$.

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Tentukan volume benda pejal dengan alas $D$ jika penampang yang tegak lurus dengan sumbu-$x$ selalu berbentuk persegi panjang dengan tinggi $\\var{b}$.

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Jika $V_1$ menyatakan volume benda pejal dengan alas $D$ jika penampang yang tegak lurus dengan sumbu-$x$ selalu berbentuk persegi dan $V_2$ menyatakan volume benda pejal dengan alas $D$ jika penampang yang tegak lurus dengan sumbu-$x$ selalu berbentuk setengah lingkaran. Hitung $\\dfrac{V_1}{V_2}$.

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Waktunya 5 menit lagi ya.

Selamat datang!

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Silakan gunakan set soal ini dengan bijak. Kalian bisa mencoba set soal ini terus-menerus.

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Set soal ini dapat digunakan oleh siapapun secara gratis.

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Petunjuk pengerjaan soal:

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• Jawaban dapat dituliskan dalam bentuk desimal maupun pecahan.
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• Jika jawaban dituliskan dalam bentuk desimal, pisahkan dengan tanda titik dan bulatkan hingga dua angka di belakang titik. Contoh: ketik 0.67 untuk menjawab \$$\\frac{2}{3}\$$.
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• Jika jawaban dituliskan dalam bentuk pecahan, pisahkan pembilang dan penyebut dengan garis miring dan jawab dengan pecahan paling sederhana. Contoh: ketik 2/3 untuk menjawab \$$\\frac{2}{3}\$$.
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Jika ada kunci jawaban yang salah, kalian dapat memberitahu kami di Instagram @meongmeongproject atau OA Line @eog7710d.

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