Re: [考古] 高大96
※ 引述《reideen107 (理想一直都在)》之銘言：
: 7.Find (b) ∫(x+4) / x(x-2)(x+5) dx
: 算出來是 -2lnx/3 + 3ln(x-2)/5 + ln(x+3)/15
: 答案對嗎？...不太會這種類型的題目@@
x + 4 A B C
令 ------------- = --- + ----- + -----
(x)(x-2)(x+5) x x - 2 x + 5
則 x + 4 = (A)(x-2)(x+5) + (B)(x)(x+5) + (C)(x)(x-2)
= (A + B + C)(x^2) + (3A + 5B - 2C)(x) - 10A
A + B + C = 0 ------(1)
3A + 5B - 2C = 1 ------(2)
-10A = 4 ------(3)
-2
(3) => A = --- 代入(1)和(2)
5
2
B + C = --- ------(4)
5
11
5B - 2C = ---- -------(5)
5
3
(4)*2 + (5) => 7B = 3 => B = --- 代入(4)得
7
2 3 14 - 15 -1
C = --- - --- = --------- = ----
5 7 35 35
x+4 -2 1 3 1 1 1
------------- = (---)(---) + (---)(-----) - (----)(-----)
(x)(x-2)(x+5) 5 x 7 x - 2 35 x + 5
x+4
∫------------- dx
(x)(x-2)(x+5)
-2 1 3 1 1 1
= ∫(---)(---) + (---)(-----) - (----)(-----) dx
5 x 7 x - 2 35 x + 5
-2 3 1
= (---)(ln|x|) + (---)(ln|x-2|) - (----)(ln|x+5|) + c
5 7 35
: 5.(a) Find the volume of the solid generated by revolving the region
: between the y-axis and the curve x=2/y , 1≦y≦4 , about the y-axis.
: (b)The region in the first quadrant enclosed by the parabola y=x^2 ,
: the y-axis and the line y=1 is revolved about the line x=3/2 to
: generate a solid. Find the volume of the solid.
: 9.Find the area of the region that lies inside the circle r=1 and
: outside the cardioid r=1-cosθ.
: 煩請各位大大幫忙講解..........感謝
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