Question

由曲线y=1/x,y方=x与直线x=2,y=0围成的阴影部分面积怎么求（用定积分）

Answer 1

S = S₁ + S₂

= [x = 0,x = 1,y = 0,y = √x] + [x = 1,x = 2,y = 0,y = 1/x],括号里是线所包围的区域.

= ∫(0~1) √x dx + ∫(1~2) 1/x dx

= (2/3)x^(3/2) |(0~1) + lnx |(1~2)

= 2/3 + ln2 ≈ 1.3598