匿名
匿名 發問於 科學及數學數學 · 1 十年前

Definite integral

1.

Find the value of c that satisfies the integral equation ∫(0 to c) |x^2-1|dx = c

(Assume that c>0)

更新:

咁快做完???

4 個解答

評分
  • 1 十年前
    最愛解答

    1.Findthe value of c that satisfies the integral equation∫(0 to c) |x^2-1|dx = c

    (Assume that c>0)

    Sol

    ∫(0 to c)_|x^2-1|dx

    (1) 1>c>0

    ∫(0 to c)_|x^2-1|dx

    =∫(0 to c)_1-x^2dx

    =x-x^3/3|(0 to c)

    =c^3/3-c=c

    c^3/3=2c

    c^2=6(reject)

    (2) c>1

    ∫(0 to c)_|x^2-1|dx

    =∫(0 to 1)_|x^2-1|dx+∫(1 to c)_|x^2-1|dx

    =∫(0 to 1)_1-x^2dx+∫(1 to c)_x^2-1dx

    =x-x^3/3|(0 to 1)+(x^3/3-x)|(1 to c)

    =[(1-1/3)-0]+[(c^3/3-c)-(1/3-1)]

    =2/3+c^3/3-c+2/3=c

    2+c^3-3c+2=3c

    c^3-6c+4=0

    (c-2)(c^2+2c-2)=0

    c=2 or c=(-2+/-√12))/2(reject)

  • 匿名
    Lv 7
    1 十年前

    抱歉 可能我還未能理解,,,,

    我需要時間消化一下,,,

    就請別的解答一下吧...

  • 需考慮 c >= 1 和 c < 1 兩 case.

  • 1 十年前

    0.732 可能不適合,請對一下.

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