Question

Luas daerah yanv dibatasi olrh parabola y=-x²+1 dan y=x²+1 adalah.....

Mohon dibantu ya

Answer 1

Verified answer

Answer 2

Verified answer

Y2 - y1 = (x^2 - 1) - (-x^2 + 1) = 2x^2 - 2
D = b^2 - 4ac = (0)^2 - 4(2)(-2) = 16
Luas = D√D / 6a^2 = 16√16 / 6(2)^2 = 16 . 4 / 6 . 4 = 16/6 = 8/3 = 2 2/3

Cara integral
Titik potong : y = y
=> x^2 - 1 = -x^2 + 1
=> 2x^2 = 2
=> x^2 = 1
=> x = ± 1 jadi x = 1 atau x = -1
Luas = integral (-x^2 + 1) - (x^2 - 1) dx
= Integral (-2x^2 + 2) dx
= -2/3 x^3 + 2x | batas -1 sampai 1
= (-2/3 (1)^3 + 2(1)) - (-2/3 (-1)^3 + 2(-1))
= (-2/3 + 2) - (2/3 - 2)
= -4/3 + 4
= (-4 + 12)/3
= 8/3
= 2 2/3