Question

∫上限b 下限a f(x)dx/[f(x)+g(x)]=1 ,则∫上限b 下限a g(x)dx/f(x)+g(x)=

Answer 1

∫(g(x)/[f(x)+g(x)]
=∫{[f(x)+g(x)-g(x)]/[g(x)+f(x)]}dx
=∫{[f(x)+g(x)]/[g(x)+f(x)]}dx-∫{g(x)/[g(x)+f(x)]}dx
=∫1dx-1
=b-a-1
(上限b,下限a,不能直接表示,就没有写下来,你应该明白是定积分.)
补充:
∫(b,a)(g(x)/[f(x)+g(x)]
=∫(b,a){[f(x)+g(x)-g(x)]/[g(x)+f(x)]}dx
=∫(b,a){[f(x)+g(x)]/[g(x)+f(x)]}dx-∫(b,a){g(x)/[g(x)+f(x)]}dx
=∫(b,a)1dx-1
=b-a-1
在积分号后的(b,a)表示上下限.