设函数f(x)=x(0≤x≤π)展开成正弦级数为∑_n=1^∞b_nsinnx，求系数b₇．

设函数f(x)=x(0≤x≤π)展开成正弦级数为∑_n=1^∞b_nsinnx，求系数b₇．

b₇=2/π∫₀^πf(x)sin7xdx =2/π∫₀^πxsin7xdx =2/(7π)(-[xcos7x]₀^π+∫₀^πcos7xdx) =2/(7π)(π+1/7[sin7x]₀^π)=2/7