x
=
0,y
=
e^0
=
1
x
=
1,y
=
1/e
绕y轴旋转,用y做自变量较方便:y
=
e^(-x),x
=
-lny
0
<
y
<
1/e时,旋转体为:截面为半径=1,高为1/e的圆柱,体积V1
=
π*1²*1/e
=
π/e
1/e
<
y
<
1处,旋转体截面为以|-lny|为半径的圆,V2
=
∫πln²ydy
=
πy(ln²y
-
2lny
+
2)
(1/e
->1)
=
π(0
-
0
+2)
-
π(1
+
2
+
2)/e
=
2π
-
5π/e
V
=
V1
+V2
=
π/e
+
2π
-
5π/e
=
2π
-
4π/e
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