Question

求曲线y=根号2x 及曲线上点（2,2）处的切线与y=0所围成的图形的面积

Answer 1

y'= 1/√(2x)

y'|(x=2) = 1/2

切线：y=1/2(x-2) +2 = 1/2 x +1

x = 2y -2

S=∫ [y²/2 - (2y -2)] dy

= [ y³/6 - y² + 2y]

= 4/3