计算累次积分I=∫21dx∫1x2yexydy
\u8ba1\u7b97\u590d\u53d8\u51fd\u6570\u7684\u79ef\u5206 w=\u222be^-z dz\uff0c\u79ef\u5206\u53f7\u4e0a\u9762\u662fi\uff0c\u4e0b\u9762\u662f0\u8fd9\u4e2a\u5f88\u7b80\u5355\u554a\uff0c\u548c\u5b9e\u6570\u7684\u79ef\u5206\u662f\u5b8c\u5168\u7c7b\u4f3c\u7684\u3002
\u222b [0\u2192i] e^-z dz
=-e^(-z) [0\u2192i]
=1-e^(-i)
=1-cos1+isin1
=f(x)=c (c\u4e3a\u5e38\u6570),\u5219f'(x)=0
f(x)=x^n (n\u4e0d\u7b49\u4e8e0) f'(x)=nx^(n-1) (x^n\u8868\u793ax\u7684n\u6b21\u65b9)
f(x)=sinx f'(x)=cosx
f(x)=cosx f'(x)=-sinx
f(x)=a^x f'(x)=a^xlna(a>0\u4e14a\u4e0d\u7b49\u4e8e1,x>0)
f(x)=e^x f'(x)=e^x
f(x)=logaX f'(x)=1/xlna (a>0\u4e14a\u4e0d\u7b49\u4e8e1,x>0)
f(x)=lnx f'(x)=1/x (x>0)
f(x)=tanx f'(x)=1/cos^2 x
f(x)=cotx f'(x)=- 1/sin^2 x
\u5bfc\u6570\u8fd0\u7b97\u6cd5\u5219\u5982\u4e0b
(f(x)+/-g(x))'=f'(x)+/- g'(x)
(f(x)g(x))'=f'(x)g(x)+f(x)g'(x)
(g(x)/f(x))'=(f(x)'g(x)-g(x)f'(x))/(f(x))^2
故交换积分顺序计算可得，
I=
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