Question

Tentukan luas daerah yang dibatasi oleh kurva y=x^2+7x+12 dan y=-x-3

Answer 1

Y = -x - 3y = x^2 + 7x + 12

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y1 = y2
x^2 + 7x + 12 = -x - 3
x^2 + 7x + x + 12 + 3 = 0
x^2 + 8x + 15 = 0
(x + 3) (x + 5) = 0

x = -3 = a (batas atas) \/ x = -5 = b(batas bawah)

(a)ʃ(b) y1 - y2
= (a)ʃ(b) x^2 + 7x + 12 - (-x - 3)
= (a)ʃ(b) x^2 + 7x + 12 + x + 3
= (a)ʃ(b) x^2 + 8x + 15x
= (a)ʃ(b) 1/3 x^3 + 4x^2 + 15x
= [x^3 + 4x^2 + 15x] - [x^3 + 4x^2 + 15x]
= [(-3)^3 + 4(-3)^2 + 15(-3)] - [(-5)^3 + 4(-5)^2 + 15(-5)]
= [(-27) + 4(9) + (-45)] - [(-125) + 4(25) + (-75)]
= [-27 + 36 - 45] - [-125 + 100 - 75]
= [-36] - [-100]
= -36 + 100
= 64 satuan luas