设f(x)在[a,b]上连续,且f(b)=a,f(a)=b,证明∫(上b下a)f(x)f'(x)dx=1/2(a²-b²)

设f(x)在[a,b]上连续,且a 设f(x)在[a,b]上连续,且a 设f(x)在[a,b]上连续,且a 设函数f(x)在[a,b]上连续,在(a,b)内可导且f'(x) 设函数f(x)在[a,b]上连续,在(a,b)上可导且f'(x) 设函数f(x),g(x)在区间[a,b]上连续,且f(a) 证明设f(x)在有限开区间(a,b)内连续,且f(a+) ,f(b-)存在,则f(x)在(a,b)上一致连续. 设函数f(x)在[a,b]上连续,在(a,b)可导,且f(a)*f(b)>0,f(a)*f((a+b)/2) 设f(x) 在[a,b] 上连续,且f(x)>0.求证:∫(a,b)f(x)dx*∫(a,bdx/f(x)≥(b-a)^2. 设f(x)在[a,b]上连续,且没有零点,证明f(x)在[a,b]上保号 设函数f(x)在[a,b]上连续,a 设f(x)在[a,b]上连续,a 设函数f(x)在[a,b]上连续,a 设f(x)在闭区间（a,b)上连续,且a 设函数f(x)在[a,b]上连续,且a 设函数f(x)在[a,b]上连续,且a 设函数f(x)在[a,b]上连续,在(a,b)内有二阶导数,且有f(a)=f(b)=0,f(c)>0(a 设f'(x)在[a,b]上连续,在（a,b)内二阶可导,且f(a)=f(b)=0,f(c)>0,a