高等数学定积分一题证明：设函数f(x)在区间[a,b]上连续,g(x)在[a,b]上连续且不变号,则在[a,b]存在一点E

函数f(x)在区间[a,b]上连续,所以有最大值与最小值,分别设为M,N.不妨设g(x)≥0N≤f(x)≤M Ng(x)≤f(x)g(x)≤Mg(x)∫[a,b] Ng(x)dx≤ ∫[a,b]f(x)g(x)dx≤ ∫[a,b]Mg(x)dxN∫[a,b] g(x)dx≤ ∫[a,b]f(x)g(x)dx≤ M∫[a...