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单选题若Ω是由球面围成的闭区域,则化三重积分为球面坐标系下的三次积分:=( )

A.

B.

C.

D.

高等数学课程封面

学科：高等数学

时间：2026-05-19 12:29:14

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声源S和接收器R在一条直线上以20m/s相同的速度沿同一方向运动,设声波的传播速度为340m/s,声源振动频率为1000Hz,则接收器测得的频率为

A. 1059HzB. 1000HzC. 941HzD. 889Hz

声源的频率为νS,声波在媒质中的传播速度为u.接收器R相对媒质静止,声源S相对于媒质以速度vS向接收器R运动,则接收器R接收到的声波频率为

A. νSB. νS(u+vS)/uC. νS(u-vS)/uD. νSu/(u-vS)

火车以60m/s的速度行驶时,在铁路旁与铁路平行的公路上有一汽车在火车后方以20m/s的速度与火车同向行驶,火车汽笛的频率为800Hz,坐在汽车中的人听到火车鸣笛声的频率为(已知空气中声速为340 m/s)

A. 847HzB. 680HzC. 720HzD. 640Hz

若Ω由z=1, <img src="https://tihai-oss-cloud.itihey.com/img/e775861f090ba0459265608deeacebc7.webp">所围成的闭区域,则<img src="https://tihai-oss-cloud.itihey.com/img/2b6ff272d3a6946309acbb132f208eb9.webp">=( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/99cf778c9503b16a19f20b3398410d9e.webp">B. <img src="https://tihai-oss-cloud.itihey.com/img/b2b93b2626a2a8e38c2a92c3c50be78e.webp">C. 0D. <img src="https://tihai-oss-cloud.itihey.com/img/5f0d0e1efd79b63006ca47dd6edef07f.webp">

若Ω由柱面<img src="https://tihai-oss-cloud.itihey.com/img/88ff4e6436a76e20bc6f396a7ca0a39e.webp">及平面z=0, 平面z=a (a>0)和平面y=0所围成,将三重积分化为柱面坐标系下的三次积分:<img src="https://tihai-oss-cloud.itihey.com/img/8771e27e5702416d29676bab78d393c7.webp">=( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/4c3517e6b113ec38dfb55069e0deff38.webp">B. <img src="https://tihai-oss-cloud.itihey.com/img/75737945b12db67a2461542a1db7f7a7.webp">C. <img src="https://tihai-oss-cloud.itihey.com/img/8a102e6f4ebe0785b62db3482f02ebff.webp">D. <img src="https://tihai-oss-cloud.itihey.com/img/4bfa7d7c75bb09b646a2dfb33f3fad70.webp">

若Ω是由球面<img src="https://tihai-oss-cloud.itihey.com/img/fcd4e3ce54fe8f94e521621f7e8db04c.webp">围成的闭区域,则化三重积分为球面坐标系下的三次积分:<img src="https://tihai-oss-cloud.itihey.com/img/4d98deb839bc0ba0c4cb9cca8da662b6.webp">=( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/111d5937ac68fc0194c4ca41ceec8111.webp">B. <img src="https://tihai-oss-cloud.itihey.com/img/91335591d46daa915f390adce521edc4.webp">C. <img src="https://tihai-oss-cloud.itihey.com/img/8c0fb99eeb993a00093835130c280913.webp">D. <img src="https://tihai-oss-cloud.itihey.com/img/06cec39a95256b01528cc94fa100e718.webp">

若Ω由<img src="https://tihai-oss-cloud.itihey.com/img/db6cb21cad482e2d07cca3a43968f07b.webp">与<img src="https://tihai-oss-cloud.itihey.com/img/1ca52323e54e9e6f2383ddc0df33ae77.webp">所围成,将三重积分化为柱面坐标系下的三次积分:<img src="https://tihai-oss-cloud.itihey.com/img/d954092ec1491bc89373a98cf1d48ad0.webp">=( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/d6d232aaa4e8d4fc50b64d8a77585bcf.webp">B. <img src="https://tihai-oss-cloud.itihey.com/img/afff21b6d2bf1fc415425f1905acc19a.webp">C. <img src="https://tihai-oss-cloud.itihey.com/img/d1a3d637206553dd6eed621023350a3b.webp">D. <img src="https://tihai-oss-cloud.itihey.com/img/ff6f8bc188f31a6437a22252b4fc2d31.webp">

若Ω是由<img src="https://tihai-oss-cloud.itihey.com/img/0b7cb108e8a2ab0c9dd797fc09c89944.webp">及 z=2 围成的闭区域,则将三重积分化为柱面坐标系下的三次积分为:<img src="https://tihai-oss-cloud.itihey.com/img/fd022eeb2f02fbc49133d8b9540b25b2.webp">=( )

A. <img src="https://tihai-oss-cloud.itihey.com/img/1b1b46b74b5b20904229ea6d559f32f7.webp">B. <img src="https://tihai-oss-cloud.itihey.com/img/0650acb12cd5cb3a0f01c8d12fc19cbb.webp">C. <img src="https://tihai-oss-cloud.itihey.com/img/fed8d53640713a4e85bc2e45339e25d6.webp">D. <img src="https://tihai-oss-cloud.itihey.com/img/c951935ff049386e41faf2a01995e9bc.webp">

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