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求两道高数积分题的解答
问题1.CalculatetheareaoftheregionDenclosedbythecurvex=y^2andthecurvey=x^2问题2.Iftheareao...
问题1. Calculate the area of the region D enclosed by the curve x=y^2 and the curve y=x^2
问题2. If the area of the region D enclosed by the curve y=x−x^2 and the curve y=kx is 9/2, then k=? 展开
问题2. If the area of the region D enclosed by the curve y=x−x^2 and the curve y=kx is 9/2, then k=? 展开
1个回答
展开全部
【0,1】∫(x²-√x)dx
=【0,1】x³-2/3x^(3/2)
=1-2/3=1/3
x-x^2=kx
x=1-k
【0,1-k】∫x-x²-kxdx
=【0,1-k】x²/2-x³/3-kx²/2
=(1-k)²/2-(1-k)³/3-k(1-k)²/2
=9/2
=【0,1】x³-2/3x^(3/2)
=1-2/3=1/3
x-x^2=kx
x=1-k
【0,1-k】∫x-x²-kxdx
=【0,1-k】x²/2-x³/3-kx²/2
=(1-k)²/2-(1-k)³/3-k(1-k)²/2
=9/2
追问
第一题对的,第二题好像不对呢
追答
你解出来k了吗?
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