help!! definite integral 問題!

=====================================================

圖片參考：http://img840.imageshack.us/img840/92/39785578.png


2010-12-11 15:37:14 補充：
http://img840.imageshack.us/img840/92/39785578.png

2010-12-11 17:01:05 補充：
第2條答案是 12.6 - (-4.26666) = 16.86666

1 ∫ x√(x^2-4) dx [from 2 to 3]=(1/2) ∫ √(x^2-4) d(x^2-4) [from 2 to 3]=(1/2)(2/3) (x^2-4)^(3/2) | [2,3]=(1/3) (x^2-4)^(3/2) [2,3]=5^(3/2)2 ∫ x^3√(x^2+4) dx [from 0 to √5]=2 ∫ x^3√((x/2)^2+1) dx [from 0 to √5]Let x/2=tan θ, when x=0, θ=0 ; when x=√5, θ=tan^(-1)(√5/2)

dx/2=(secθ)^2dθ=32 ∫ (tanθsecθ)^3 dθ [from 0 to tan^(-1)(√5/2)]=32 ∫ (sec^2 θ-1)(secθ)^2 d(secθ) [from 0 to tan^(-1)(√5/2)]=32[(secθ)^5/5-(secθ)^3/3] |[0,tan^(-1)(√5/2)]

~16.87

=112/3



2010-12-11 16:11:17 補充：
1 =5^(3/2)/3

2010-12-11 16:14:10 補充：
2 =112/3 刪去