daerah D dikuadran 1 dibatasi oleh parabola x=1/2ypangkat 2 garis x-y=4 dan sumbu X . hitunglah luas daerah D

2 per 2 - 4 ...............................................................

x - y = 4
y = x - 4

2x = y²
2x = (x - 4)²
2x = x² - 8x + 16
x² - 8x - 2x + 16 = 0
x² - 10x + 16 = 0
(x  - 8)(x - 2) = 0
x = 8    x = 2

y = √2x 
y = x - 4

[tex] \int\limits^8_2 {(x - 4) - \sqrt{2x} } \, dx [/tex]
[tex] \int\limits^8_2 {x - 4 - (2x) ^{1/2} } \, dx [/tex]
[tex][ \frac{1}{2} x^{2} - 4x - \frac{2√2}{3} x^{3/2} ][/tex]
[1/2(8)² - 4(8) - [tex] \frac{2√2}{3} (8)^{3/2} [/tex]] - [ 1/2(2)² - 4(2) - [tex] \frac{2√2}{3} (2)^{3/2} [/tex]
[32 - 32 - (2√2)/3(16√2)] - [2 - 8 - (2√2/3)(2√2)]
-32/3 + 6 + 16/3
-16/3 + 18/3 = 2/3 satuan luas