Question

这个分部积分怎么求解

要详细过程啊

Answer 1

an
=(1/π)∫(-π->π) 2x^2. cosnx dx
=(2/π)∫(0->π) 2x^2. cosnx dx
=[4/(nπ)] ∫(0->π) x^2. dsinnx
=[4/(nπ)] [x^2. sinnx]|(0->π) -[8/(nπ)] ∫(0->π) x.sinnx dx
=[8/(n^2.π)] ∫(0->π) x.dcosnx
=[8/(n^2.π)] [ x.cosnx ]|(0->π) -[8/(n^2.π)] ∫(0->π) cosnx dx
=[8/(n^2.π)][π. (-1)^n ] - [8/(n^3.π)] [sinnx]|(0->π)
=(-1)^n .( 8/n^2) - 0
=(-1)^n .( 8/n^2 )