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∫∫x√y,其中D是由两条抛物线y=√x,y=x^2所围成的闭合图形,为什么是6/55
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∫∫x√y,其中D是由两条抛物线y=√x,y=x^2所围成的闭合图形,为什么是6/55
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答案和解析
∫∫x√ydxdy
=∫[0,1]xdx∫[x^2,√x]√ydy
=∫[0,1]xdx 2/3y^(3/2) [x^2,√x]
=2/3∫[0,1]( x^(7/4)-x^4 )dx
=2/3 (4/11x^11/4-1/5x^5) [0,1]
=6/55
=∫[0,1]xdx∫[x^2,√x]√ydy
=∫[0,1]xdx 2/3y^(3/2) [x^2,√x]
=2/3∫[0,1]( x^(7/4)-x^4 )dx
=2/3 (4/11x^11/4-1/5x^5) [0,1]
=6/55
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