Question

高数，微积分，级数

Answer 1

你这个是傅里叶级数吧
∫x²cosnx dx
分部积分
=(1/n)∫x² d(sin nx)
=(1/n)[x²sin nx - ∫sin nx d(x²)]
=(1/n)[x²sin nx - ∫2x sin nx dx]
=(1/n)[x²sin nx + (2/n)∫x d(cosnx)]
=(1/n)[x²sin nx + (2/n)(xcosnx- ∫cosnx dx)]
=(1/n)[x²sin nx + (2/n)(xcosnx- (1/n) sin nx)]
再代入上下限即可。