设f(x)在[0.1]连续,证明∫(0→1)[f(x)^2]dx≥[∫(0→1)f(x)dx]^2

设f(x)在[0.1]连续,证明∫(0→1)[f(x)^2]dx≥[∫(0→1)f(x)dx]^2 设f(x)在[a,b]连续,在(a,b)可导,f'(x)≤0,F(x)=[∫(a→x)f(t)dt]/(x-a),证明在(a,b)有F'(x)≤0 设f'(x)在[a,b]上连续,证明:lim(λ→+∞)∫(a,b)f(x)cos(λx)dx=0 高数证明题：设函数f(x)在区间[0,1]上连续,证明 设函数f(x)在对称区间【-a,a】上连续,证明∫(-a,a)f(x)dx=∫(0,a)[f(x)+f(-x)]dx 设f(x)在(-无穷,+无穷)内连续,证明(d/dx)∫(0~x)(x-t)f'(t)dt=f(x)-f(a) 证明：设f(x)在(-∞,+∞)连续,则函数F(x)=∫(0,1)f(x+t)dt可导,并求F'(x) 证明：设f(x)在x=0连续,且lim(x→0) (f(x)/x)=1,则必有f'(0)=1 设f(x)在区间【0,1】上有连续导数,证明x∈【0,1】,有|f(x)|≤∫(|f(t)|+|f′(t)|)dt 设f(x)在区间【0,1】上有连续导数,证明x∈【0,1】,有|f(x)|≤∫(|f(t)|+|f′(t)|)dt f(x)在(0.1)上连续且单调增,证明∫[0,1]f(x)dx 求设f'(x)在[0,a]上连续.f(0)=0,证明|定积分f(x)d(x) 设f(x)在区间(-∞,+∞)内单调增加,limf(x)=1（x→0）,证明f(x)在x=0处连续 证明:设f(x)在[a,b]上连续,在(a,b)内可导,(0 设F(X)在[0,1]中连续,证明 ∫0~1/2 f(1-2x)dx =1/2∫0~1 f(X)dx 设函数f(x)在[A,B]上连续,证明lim(h→0) 1/h*∫(x,a)[f(t+h)-f(t)]dt=f(x)-f(a),其中A 设f(x)在[-a,a]( a>0,a为常数)上连续,证明:∫(-a→a)f(x)dx=∫(0→a)[f(x)+f(-x)]dx 设f(x)在[0,1]上有连续导数,且f(x)=f(0)=0.证明