两曲线y=x²与y=cx³(c>0)围成面积为2/3,则c=?
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两曲线y=x²与y=cx³(c>0)围成面积为2/3,则c=?
两曲线y=x²与y=cx³(c>0)围成面积为2/3,则c=?
两曲线y=x²与y=cx³(c>0)围成面积为2/3,则c=?
两曲线的交点
(0,0),(1/c,1/c^2)
运用定积分得
∫[0,1/c](x^2-cx^3)dx
=(x^3/3-cx^4/4)[0,1/c]
=1/(3c^3)-1/(4c^3)
=1/(12c^3)
=±2/3
c^3=±1/18
c=三次根号(1/18)