设M=∫上限是π/2下限是0,sin(sinx)dx,N=∫上限是π/2下限是0,cos(cosx)dx则是M<1<N为什么,要过

问题描述:

设M=∫上限是π/2下限是0,sin(sinx)dx,N=∫上限是π/2下限是0,cos(cosx)dx则是M<1<N为什么,要过

楼主你好
正解
M=∫[0,π/2] sin(sinx)dx
∵ 0∴ M N=∫[0,π/2] cos(cosx)dx =∫[0,π/2] cos(sint)dt [令:x=π/2 -t]
∵ 0 cos(sint)>cost
∴ M >∫[0,π/2] cost dx =1

M=∫[0,π/2] sin(sinx)dx
∵ 0