※ 引述《alasa15 (alasa)》之銘言：
: 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
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 114.34.122.244
※ 編輯: rygb 來自: 114.34.122.244 (07/07 12:36)
→
07/07 12:51, , 1F
07/07 12:51, 1F
討論串 (同標題文章)