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17Volume of revolution A-level考试纯数学P1课件.ppt

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Chapter17Volumeofrevolution

VolumesofrevolutionxyAOxyAO

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Whentheregionunderthegraphofy=f(x)betweenx=aandx=b(whereab)isrotatedaboutthex-axis,thevolumeofthesolidofrevolutionformedis

ExampleFindthevolumegeneratedwhentheregionunderthegraphofy=1+x2betweenx=-1andx=1isrotatedthroughfourrightanglesaboutthex-axis.

ExampleProvethatthevolumeVofaconewithbaseradiusrandheighthis

Volumesofrevolutionaboutthey-axisxyOdcy=f(x)xyOdcWhentheregionboundedbythegraphofy=f(x),thelinesy=candy=dandthey-axisisrotatedaboutthey-axis,thevolumeofthesolidofrevolutionformedis

ExampleFindthevolumegeneratedwhentheregionboundedbyy=x3andthey-axisbetweeny=1andy=8isrotatedthrough360°aboutthey-axis.

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