高数二重积分题：计算由平面x=0,y=0,x=1,y=1所围成的柱体被平面z=0,2x+3y+z=6
\u9ad8\u6570\u4e8c\u91cd\u79ef\u5206\u9898\uff1a\u8ba1\u7b97\u7531\u5e73\u9762x=0,y=0,x=1,y=1\u6240\u56f4\u6210\u7684\u67f1\u4f53\u88ab\u5e73\u9762z=0,2x+3y+z=6\u622a\u5f97\u7684\u7acb\u4f53\u4f53\u79ef\u672c\u9898\u662f\u4e00\u4e2a\u66f2\u9876\u67f1\u4f53\u7684\u4f53\u79ef\uff0c\u7ed3\u679c\u4e3a\u4e8c\u91cd\u79ef\u5206\uff0c\u79ef\u5206\u533a\u57df\u662f\u5e95\u9762\uff0c\u4e5f\u5c31\u662f0<=x<=1\uff0c0<=y<=1
\u88ab\u79ef\u51fd\u6570\u662f\u9876\u9762\u65b9\u7a0b\uff1az=6-2x-3y\uff0c\u505a\u4e8c\u91cd\u79ef\u5206\u5c31\u53ef\u4ee5\u4e86\u3002\uff08\u672c\u9898\u7528\u4e09\u91cd\u79ef\u5206\u505a\u4e5f\u53ef\u4ee5\uff09
\u222b\u222b(6-2x-3y)dxdy
=\u222b[0,1]\u222b[0,1] (6-2x-3y)dxdy
=\u222b[0,1] (6x-x^2-3xy) dy [x\u75281\uff0c0\u4ee3\u5165\u76f8\u51cf]
=\u222b[0,1] (5-3y) dy
=5y-(3/2)y^2 [y\u75281\uff0c0\u4ee3\u5165\u76f8\u51cf]
=5-(3/2)=7/2
1 1
\u222b \u222b \uff086-2x-3y\uff09dxdy=3.5
0 0
\u5982\u679c\u6ca1\u5b66\u8fc7\u9ad8\u7b49\u6570\u5b66\uff0c\u90a3\u4e48\u539f\u7acb\u4f53\u662f\u4eceX=0,Y=0,X=1,Y=1,Z=0,Z=6\u8fd9\u4e2a\u957f\u65b9\u4f53\u4e0a\u5207\u4e0b\u4e00\u5757\u6765\uff0c\u800c\u5207\u4e0b\u6765\u7684\u8fd9\u4e00\u5757\u4f53\u79ef\u5c31\u662f\u5e95\u9762\u79ef\u4e3a1\uff0c\u9ad8\u4e3a5\u7684\u957f\u65b9\u4f53\u7684\u4e00\u534a\uff0c\u6240\u4ee5\u539f\u4f53\u79ef=6-5/2=3.5
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