作者rygb (再生)
看板Math
标题Re: [微积] 一题体积分
时间Thu Jul 7 12:36:01 2011
※ 引述《alasa15 (alasa)》之铭言：
: Evaluate
: ∫∫∫ (x^2+y^2)^0.5 dV, where B is the volumn bounded by z=x^2+y^2
: B and z=4
: I do this problem in two ways, but i got two different answers.
: Method I. ∫∫ (x^2+y2)0.5 * [4-x^2-y^2] dxdy
: D
: Method II. Let x=r cost, y=r sint, z=z => |J| = r
: 2π 2 2
: ∫ ∫ ∫ (r^2)^0.5 * r dy dr dt
: 0 0 0
: which is correct?
: (I think there are some mistakes in Method II..)
Yeah, Method II got a little mistake, your "z" interval is wrong
in yours , the volume just means "cylinder"
but the correct one is z = r^2 ~ 4
you can try to draw a picture when you not sure.
Or you can put x=rcost , y = r sint inside the condition
and you will get.
z = r^2 and z = 4
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◆ From: 114.34.122.244
※ 编辑: rygb 来自: 114.34.122.244 (07/07 12:36)
1F：→ alasa15 :THANKS A LOT! 07/07 12:51