Question

F(x) = -x² + 18 dan g(x) = x², luas antara f(x) dan g(x) adalah ....

Answer 1

Verified answer

F(x) = -x² + 18
g(x) = x²

titik potong f(x) dan g(x)
-x² + 18 = x²
2x² - 18 = 0
x² - 9 = 0
(x + 3) (x - 3) = 0
x = -3   x = 3

jadi luas antara f(x) dan g(x) adalah
∫ -2x² + 18  dx  ...{-3 ... 3}
= -2x³/3 + 18x   {-3 ... 3}
= [-2(3)³/3 + 18(3)] - [-2(-3)³/3 + 18(-3)]
= [-18 + 18(3)] - [18 + 18(-3)]
= [18 (-1 + 3)] - [18 (1 - 3)]
= [18 (2)] - [18 (-2)]
= 36 + 36
= 72 satuan luas.