Question

Luas daerah yang dibatasi parabola y=x^2 - 6x +7 dan garis y=2x-8 adalah....

Answer 1

Cari batasnya dulu:
x² - 6x + 7 = 2x - 8
x² - 8x + 15 = 0
(x - 3)(x - 5) = 0
x = 3 atau x = 5

Luas = int [3 - 5] {(2x - 8) - (x² - 6x + 7)} dx
= int [3 - 5] (-x² + 8x - 15) dx
= (-1/3)x³ + 4x² - 15x [3 - 5]
= ((-1/3)(125) + 100 - 75) - ((-1/3)(27) + 36 - 45))
= (-125/3 + 25) - (-27/3 - 9)
= - 98/3 + 34
= -98/3 + 102/3
= 4/3 satuan luas