Question

sinx^6/（sinx^6+cosx^6）不定积分？

Answer 1

目测本题应该是0→π/2的定积分.,1,
瞬间陌尘 举报
额。如果是定积分怎么做？ 用一个结论：∫[0→π/2] f(sinx) dx = ∫[0→π/2] f(cosx) dx 因此： ∫[0→π/2] (sinx)^6/[(sinx)^6+(cosx)^6] dx =∫[0→π/2] (cosx)^6/[(sinx)^6+(cosx)^6] dx =(1/2){ ∫[0→π/2] (sinx)^6/[(sinx)^6+(cosx)^6] dx + ∫[0→π/2] (cosx)^6/[(sinx)^6+(cosx)^6] dx } =(1/2)∫[0→π/2] 1 dx =π/4 定积分与不定积分的差异是很大的，不能随便把定积分的题当作不定积分来问。,次方在里面还是外面？究竟是sin^6(x)还是sin(x^6)？是（sinx）^6令A=∫sin^6(x)/(sin^6(x)+cos^6(x))dx，B=∫cos^6(x)/(sin^6(x)+cos^6(x))dx， 则A+B=∫dx=x+C， A-B=∫(sin^2(x)-cos^2(x))*(sin^4(x)+sin^2(x)cos^2(x)+cos^4(x))/(sin^2(x)+c...,1,