利用定义式直接进行积分，对于容易求积分的函数比较有效。（ ）

A . 正确 B . 错误

A . 正确 B . 错误

A . A、二 B . B、三 C . C、四

A . 分划、取点、作和、取极限 B . 作差、作商、取极限 C . 分划、取点、作商、取极限 D . 作差、作积、取极限

A . A、A B . B、B C . C、C D . D、D

<img src='https://img2.soutiyun.com/ask/2020-12-20/977328821805932.png' />

求连续函数(x),使它满足积分方程<img src='https://img2.soutiyun.com/ask/2020-12-13/976734813945554.png' />注;未知函数含在积分号下面的方程,称为积分方程.

试用二重积分定义求极限<img src='https://img2.soutiyun.com/ask/2020-12-15/976873327958872.png' />其中D是圆域:<img src='https://img2.soutiyun.com/ask/2020-12-15/976873339405527.png' />最大整数，n是正整数。

<img src='https://img2.soutiyun.com/ask/2020-08-14/96624425787688.png' />

设f(x)为[0,1]上的非负单调非增连续函数(即当x＜y时,f(x)≥f(y)).利用积分中值 定理证明:对于0＜a＜β＜1.有下面的不等式成立 <img src='https://img2.soutiyun.com/ask/2020-11-30/975612485146551.png' />

定义在[a，b]上的无界函数f(x)的收敛，积分<img src='https://img2.soutiyun.com/latex/latex.action' />是否可以视为相应积分和数<img src='https://img2.soutiyun.com/latex/latex.action' />(这里x_i≤ξ_i≤x_i+1且△x_i=x_i+1-x_i)的极限？

计算下列积分(利用留数，圆周均取正向)． <img src='https://img2.soutiyun.com/ask/uploadfile/9075001-9078000/1504c20edfe66d1baeae69b67472a287.jpg' />

已知微分方程 (x2+y)dx+f(x)dy=0 有积分因子μ=x，试求所有可能的函数f(x)．

<img src='https://img2.soutiyun.com/ask/2020-12-28/977993945514249.jpg' /> <img src='https://img2.soutiyun.com/ask/2020-12-28/977993961306152.jpg' /> <img src='https://img2.soutiyun.com/ask/2020-12-28/977994003441562.jpg' />

<img src='https://img2.soutiyun.com/ask/2020-11-25/975176796384511.png' />

<img src='https://img2.soutiyun.com/ask/2021-01-19/979915120559503.png' />

已知<img src='https://img2.soutiyun.com/ask/2021-01-13/979416083675346.png' />试利用此结果求下列积分: <img src='https://img2.soutiyun.com/ask/2021-01-13/97941610087333.png' /> <img src='https://img2.soutiyun.com/ask/2021-01-13/979416110911904.png' />

<img src='https://img2.soutiyun.com/ask/2020-11-02/973173912091949.png' />