请问这道高数面积题怎么做 麻烦画一下图?
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x=√y (1)
x=√(2-y^2) (2)
y=0 (3)
from (1) and (2)
√y = √(2-y^2)
y=2-y^2
y^2+y-2=0
(y+2)(y-1) =0
y=-2(rej) or 1
Vy
=π[ ∫(0-> 1) (2-y^2) dy -∫(0-> 1) y dy ]
=π [ 2y - (1/2)y^2 - (1/3)y^3]|(0-> 1)
=π ( 2 -1/2 -1/3)
=π(12-3-2)/6
=7π/6
x=√(2-y^2) (2)
y=0 (3)
from (1) and (2)
√y = √(2-y^2)
y=2-y^2
y^2+y-2=0
(y+2)(y-1) =0
y=-2(rej) or 1
Vy
=π[ ∫(0-> 1) (2-y^2) dy -∫(0-> 1) y dy ]
=π [ 2y - (1/2)y^2 - (1/3)y^3]|(0-> 1)
=π ( 2 -1/2 -1/3)
=π(12-3-2)/6
=7π/6
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