Question

高数定积分求解

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Answer 1

希望写的比较清楚

追答

拍个清楚的，望采纳

追问

谢谢

现在像你这么热心的人回答不多了

我的意思是回答的这么详细

追答

不客气

Answer 2

对方程求微分得e^(y^2)dy=-2xcos(x^2)dx-2ysin(y^2)dy,

整理得[e^(y^2)+2ysin(y^2)]dy=-2xcos(x^2)dx,

所以dy=-2xcos(x^2)dx/[e^(y^2)+2ysin(y^2)].

Answer 3

Answer 4

(5)
(x²+x+1)/(x-1)=[x(x-1)+2(x-1)+3]/(x-1)
=x+2+3/(x-1)
lim(x→∞)｛[(x²+x+1)/(x-1)]sin(1/x)｝
=lim(x→∞) xsin(1/x) + 2lim(x→∞) sin(1/x) +3lim(x→∞) sin(1/x)/(x-1)
=lim(x→∞) xsin(1/x)
=lim(x→∞) sin(1/x) /(1/x)
=lim(x→∞) cos(1/x)
=1
∫0→+∞ k/(x²+1)dx
=karctanx|0→+∞
=kπ/2=1

k=2/π

(7)两边同时对x求导得
e^y² dy/dx=-2xcosx²-2ysiny²dy/dx
(e^y²+2ysiny²)dy=-2xcosx²dx
dy=-2xcosx²dx/(e^y²+2ysiny²)