如图,直线y=kx分抛物线y=x-x^2与x轴所围成图形为面积相等的两部分,求k值如图,由 {y=kxy=x-x2得 {x=1-ky=k-k2(0<k<1).由题设得∫01-k[(x-x2)-kx]dx=12∫01(x-x2)dx即∫01-k[(x-x2)-kx]dx=12( 12x2-13x3
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![如图,直线y=kx分抛物线y=x-x^2与x轴所围成图形为面积相等的两部分,求k值如图,由 {y=kxy=x-x2得 {x=1-ky=k-k2(0<k<1).由题设得∫01-k[(x-x2)-kx]dx=12∫01(x-x2)dx即∫01-k[(x-x2)-kx]dx=12( 12x2-13x3](/uploads/image/z/2540764-28-4.jpg?t=%E5%A6%82%E5%9B%BE%2C%E7%9B%B4%E7%BA%BFy%3Dkx%E5%88%86%E6%8A%9B%E7%89%A9%E7%BA%BFy%3Dx-x%5E2%E4%B8%8Ex%E8%BD%B4%E6%89%80%E5%9B%B4%E6%88%90%E5%9B%BE%E5%BD%A2%E4%B8%BA%E9%9D%A2%E7%A7%AF%E7%9B%B8%E7%AD%89%E7%9A%84%E4%B8%A4%E9%83%A8%E5%88%86%2C%E6%B1%82k%E5%80%BC%E5%A6%82%E5%9B%BE%2C%E7%94%B1+%7By%3Dkxy%3Dx-x2%E5%BE%97+%7Bx%3D1-ky%3Dk-k2%EF%BC%880%EF%BC%9Ck%EF%BC%9C1%EF%BC%89%EF%BC%8E%E7%94%B1%E9%A2%98%E8%AE%BE%E5%BE%97%E2%88%AB01-k%5B%EF%BC%88x-x2%EF%BC%89-kx%5Ddx%3D12%E2%88%AB01%EF%BC%88x-x2%EF%BC%89dx%E5%8D%B3%E2%88%AB01-k%5B%EF%BC%88x-x2%EF%BC%89-kx%5Ddx%3D12%EF%BC%88+12x2-13x3)
如图,直线y=kx分抛物线y=x-x^2与x轴所围成图形为面积相等的两部分,求k值如图,由 {y=kxy=x-x2得 {x=1-ky=k-k2(0<k<1).由题设得∫01-k[(x-x2)-kx]dx=12∫01(x-x2)dx即∫01-k[(x-x2)-kx]dx=12( 12x2-13x3
如图,直线y=kx分抛物线y=x-x^2与x轴所围成图形为面积相等的两部分,求k值如图,
由 {y=kxy=x-x2得 {x=1-ky=k-k2(0<k<1).
由题设得∫01-k[(x-x2)-kx]dx=12∫01(x-x2)dx即∫01-k[(x-x2)-kx]dx=12( 12x2-13x3)|01=112
∴(1-k)^3=1/23=12
∴k=1-2倍3次根号4
∴直线方程为y=(1-2倍3次根号4)x.
故k的值为:k=1-2分之3次根号4
∴k=1-2分之3次根号4
∴直线方程为y=(1-2分之3次根号4)x.
故k的值为:k=1-2分之3次根号4
(1-k)^3=1/2咋来的
如图,直线y=kx分抛物线y=x-x^2与x轴所围成图形为面积相等的两部分,求k值如图,由 {y=kxy=x-x2得 {x=1-ky=k-k2(0<k<1).由题设得∫01-k[(x-x2)-kx]dx=12∫01(x-x2)dx即∫01-k[(x-x2)-kx]dx=12( 12x2-13x3
y=kx,y=x-x² 得 x=1-k .
由题设得∫[0,1-k][(x-x²)-kx]dx=﹙1/2﹚∫[01](x-x²)dx
∫[0,1-k][(x-x²)-kx]dx=[﹙1-k﹚/2]x²-x³/3]|﹙0,1-k﹚=﹙1-k﹚³/6
﹙1/2﹚∫[01](x-x²)dx=﹙1/2﹚( x²/2-x³/3)|﹙0,1﹚=1/12
∴﹙1-k﹚³/6=1/12 ﹙1-k﹚³=1/2