⑩天掌 Teaching Plan on Advanced Mathematics o f(x)可逐项积分, 广r(xk=2f(xM+ ∑叮∫anf(x) cos ndx+bf(x) sin ndx = ∫(xx πb T ∑1f(x)osn+(x) sin ndx 广r(xk=2+2(2+),结论可证 tianjin polytechnic dmivendityTianjin Polytechnic University Teaching Plan on Advanced Mathematics  f (x)可逐项积分， +   − f x dx a ( ) 2 0  =   − f (x)dx 2     =  −  − + 1 [ ( )cos ( )sin ] n an f x nxdx bn f x nxdx = +   − f x dx a ( ) 2 0     =  −  − + 1 [ ( )cos ( )sin ] n an f x nxdx bn f x nxdx 0 a n a bn ( ) , 2 ( ) 1 2 2 2 2 0    =  − +  +    = n an bn a f x dx 结论可证