证明:若函数f（x)在[a,b]可积,则函数[f（x)]²在[a,b]也可积.

设f（x）为奇函数，且在区间[-a,a]（a＞0）上可积，则（）。 <img src='https://img2.soutiyun.com/ask/2021-01-14/979493206007165.png' />

A.必要条件 B.充分条件 C.充分必要条件 D.无关条件

函数f(x)在[a,b]上有定义且|f(x)|在[a,b]上可积,此时积分<img src='https://img2.soutiyun.com/ask/2020-11-13/974108696004819.png' />f(x)dx_______存在_______.

证明:若函数f(x)在[a,b]连续、非负,且<img src='https://img2.soutiyun.com/ask/2020-11-12/97406224084526.png' />使f(x0)＞0,则 <img src='https://img2.soutiyun.com/ask/2020-11-12/974062250390806.png' />

证明:若函数f(x)在a连续,则函数 <img src='https://img2.soutiyun.com/ask/2020-11-11/973957882099598.png' /> 在a都连续.

证明.若函数f(x)在区间[-π,π]可积,且a_k,b_k,是函数f(x)的傅里叶系数,则<img src='https://img2.soutiyun.com/ask/2020-11-13/974121166578095.jpg' />有不等式 <img src='https://img2.soutiyun.com/ask/2020-11-13/974121183156043.png' /> 后者称为贝塞尔①不等式.(证明1),讨论积分<img src='https://img2.soutiyun.com/ask/2020-11-13/974121199972005.png' />

是 否

证明:若函数f(x)＞0,在[a,b]可积,令<img src='https://img2.soutiyun.com/ask/2020-11-13/974108578848118.png' />则 <img src='https://img2.soutiyun.com/ask/2020-11-13/974108619490443.png' />

证明:若函数f(x)与φ(x)在[a,b]连续,则 <img src='https://img2.soutiyun.com/ask/2020-11-12/974060778329609.png' />

证明：若f(x)在[α，b]上可积，[α，β]真包含于[α，b]，则f(x)在[α，β]上也可积。

证明:若函数y=f(x)在[a,b]严格增加,且连续则反丽数x=f^-1(y)在点a=f(a)右连续,即 <img src='https://img2.soutiyun.com/ask/2020-11-11/973957297199144.png' />

A．单调减少,曲线是凹的 B．单调增加,曲线是凹的 C．单调减少,曲线是凸的 D．单调增加，曲线是凸的

若函数f(x)在[a,b]上可积，证明存在折线函数列<img src='https://img2.soutiyun.com/ask/2021-01-22/98018065819823.png' />

A．充分必要条件 B．充分条件,但非必要条件 C．必要条件,但非充分条件 D．既非必要条件,也非充分条件

证明:若函数f(x)在[a,b]单调增加,则 <img src='https://img2.soutiyun.com/ask/2020-11-12/974060207561962.png' />

证明:(1)若函数f在[a,b]上可导,且f'(x)≥m,则 <img src='https://img2.soutiyun.com/ask/2021-02-04/98128598322409.png' /> (2)若函数f在[a,b]上可导,且 <img src='https://img2.soutiyun.com/ask/2021-02-04/981285989538451.png' /> (3)对任意实数x₁,x₂,都有 <img src='https://img2.soutiyun.com/ask/2021-02-04/981286001647143.png' />