作业帮∫(0,10π)[(sinx)^3]/[2(sinx)^2+(cosx)^4]dx
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/02 13:29:20
![∫(0,10π)[(sinx)^3]/[2(sinx)^2+(cosx)^4]dx](/uploads/image/z/7057758-30-8.jpg?t=%E2%88%AB%280%2C10%CF%80%29%5B%28sinx%29%5E3%5D%2F%5B2%28sinx%29%5E2%2B%28cosx%29%5E4%5Ddx)
∫(0,10π)[(sinx)^3]/[2(sinx)^2+(cosx)^4]dx
∫(0,10π)[(sinx)^3]/[2(sinx)^2+(cosx)^4]dx
∫(0,10π)[(sinx)^3]/[2(sinx)^2+(cosx)^4]dx
分母=2-2（cosx)^2+(cosx)^4=1+(1-(cosx)^2)^2=1+(sinx)^4
则在（0,2π）区间对称,奇函数.故该定积分=0