答案：解析: (1)eq \a\vs4\al(\i\in(1,2,))eq \b\lc\(\rc\)(\a\vs4\al\co1(x-x2 \f(1,x)))dx=eq \a\vs4\al(\i\in(1,2,))xdx-eq \a\vs4\al(\i\in(1,2,))x2dx eq \a\vs4\al(\i\in(1,2,))eq \f(1,x)dx=eq \f(x2,2)eq \b\lc\|\rc\ (\a\vs4\al\co1(\o\al(2,1)))-eq \f(x3,3)eq \b\lc\|\rc\ (\a\vs4\al\co1(\o\al(2,1))) ln x|eq \o\al(2,1)=eq \f(3,2)-eq \f(7,3) ln 2=ln 2-eq \f(5,6).(2)==sin xeq \b\lc\|\rc\|(\a\vs4\al\co1(\o\al(0,-π) ex))eq \o\al(0,-π)=1-eq \f(1,eπ).(3)eq \i\in(4,9,)eq \r(x)(1 eq \r(x))dx=eq \i\in(4,9,)(xeq \f(1,2) x)dx=eq \b\lc\ \rc\|(\a\vs4\al\co1(\b\lc\(\rc\)(\a\vs4\al\co1(\f(2,3)x\f(3,2) \f(1,2)x2))))49=eq \f(2,3)×9eq \f(3,2)-eq \f(2,3)×4eq \f(3,2) eq \f(1,2)×92-eq \f(1,2)×42=45eq \f(1,6).(4)eq \i\in(0,π,)cos2eq \f(x,2)dx=eq \i\in(0,π,)eq \f(1 cosx,2)dx=eq \f(1,2)x|0π eq \f(1,2)sinx|0π=eq \f(π,2).
