设f（x）在【0,1】上连续.证明∫（π/2~0)f(cosx)dx=∫（π/2~0)f（sinx）dx

设f（x）在【0,1】上连续.证明∫（π/2~0)f(cosx)dx=∫（π/2~0)f（sinx）dx 若f(x)在[0,1]上连续,证明 ∫【上π/2下0】f(sinx)dx= ∫【上π/2下0】f(cosx)dx 设f(x)连续,证明（积分区间为0到2π）∫xf(cosx)dx=π∫f(sinx)dx 设f(x)导数在【-1,1】上连续,且f(0)=1,计算∫【f（cosx）cosx-f‘（cosx）sin^2x】dx（ 证明题f(u,v)在区域D=上连续,证明∫(π/2)(0)f(sinx,cosx)dx=∫(π/2)(0)f(cosx, 设f(x)连续,证明（积分区间为0到π）∫xf(sinx)dx=(π/2)∫f(sinx)dx 证明：若函数f(x)在[0,1]上连续,则∫xf(sinx)dx=π/2∫f(sinx)dx (上限 π,下限 0) ∫f（sinx,cosx）dx=∫f（cosx,sinx）dx上下限是[0,π/2] 设f(x)∈C[0,1],证明∫（π,0）*x*f(sinx)dx =π/2*∫（π,0）*f(sinx)dx 100分求高数积分题设f(x)在[-π,π]上连续 且f(x)=x/(1+(cosx)^2)+∫ f(x)sinX dx 设f(x)为连续函数,证明:∫(0,π)f(丨cosx丨)dx=2∫(0,π/2)f(sinx)dx 特急：设函数f(x)在区间[0,2a]上连续,证明：∫ f(x)dx)=∫ [f(x)+f(2a-x)]dx,