MATH QUIZ

Jawaban:

49/6 SL

Penjelasan dengan langkah-langkah:

sama ga?

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Aplikasi Integral

• luas

Parabola

y = x² – 3x

• daerah arsiran 1 = L1

L1 kiri = L3 kanan

= ∫y dx [4 3]

= ∫(x² – 3x) dx

= 1/3 x³ – 3/2 x²

= 1/3 (4³ – 3³) – 3/2 (4² – 3²)

= 1/3 (64 – 27) – 3/2 (16 – 9)

= 37/3 – 21/2

= (74 – 63)/6

= 11/6 satuan luas

•

daerah arsiran 2 (tengah) = L2

#cara 1 dg diskriminan

y = x² – 3x

D = b² – 4ac

D = (-3)² – 4.1.0

D = 9

L2 = D√D /6a²

L2 = 9√9 / 6.1²

L2 = 9/2 satuan luas

#cara 2 dg integral

L2

= ∫-(x² – 3x) dx [3 0]

= 3/2 x² – 1/3 x³

= 3/2 (3² – 0²) – 1/3 (3³ – 0³)

= 27/2 – 27/3

= 27 (3 – 2)/6

= 27/6

= 9/2 satuan luas

•

Luas total arsiran

= L1 + L2 + L3

= 2 × 11/6 + 9/2

= 22/6 + 9/2

= (22 + 27)/6

= 49/6

= 8 1/6 satuan luas