x^ 3(sin x )^2/x^ 4+2x +1在[-1,1]的定积分
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x^3(sinx)^2/x^4+2x+1在[-1,1]的定积分x^3(sinx)^2/x^4+2x+1在[-1,1]的定积分x^3(sinx)^2/x^4+2x+1在[-1,1]的定积分你好!题目可能
x^ 3(sin x )^2/x^ 4+2x +1在[-1,1]的定积分
x^ 3(sin x )^2/x^ 4+2x +1在[-1,1]的定积分
x^ 3(sin x )^2/x^ 4+2x +1在[-1,1]的定积分
你好!题目可能有错,应该是x^ 4+2x^2 +1才对吧!
因为f(x)=x^ 3(sin x )^2/(x^ 4+2x^2 +1)
=x^3(sinx)^2/(x^2+1)^2
那么f(-x)=-x^3(sinx)^2/(x^2+1)^2=-f(x)
所以被积函数为奇函数,且被积分区间为对称区间,所以
∫[-1,1]x^ 3(sin x )^2/(x^ 4+2x^2 +1)dx=0
满意请采纳,谢谢~
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