If you have a quantity which is constant over any closed path, that quantity is a thermodynamics state function.

如果有一个物理量,对任何闭合回路积分是常数，这个物理量就是一个热力学态函数。

麻省理工公开课 - 热力学与动力学课程节选

So for the reversible process, the work done is the integral under the pressure volume state function, the function of state.

对可逆过程，做的功,是压强体积态函数曲线下，的积分面积。

麻省理工公开课 - 热力学与动力学课程节选

What's a function, what's a derivative, what's a second derivative, how to take derivatives of elementary functions, how to do elementary integrals.

什么是函数,什么是导数,什么是二阶导数,如何对初等函数求导,如何进行初等积分

耶鲁公开课 - 基础物理课程节选

Cv So, for Cp and Cv, these are often quantities that are measured as a function of temperature, and one could, in fact, calculate this integral.

一般Cp和,都是温度的函数，因此实际上，我们可以将这个积分计算出来。

麻省理工公开课 - 热力学与动力学课程节选

In other words, your job is to guess a function whose second derivative is a, and this is called integration, which is the opposite of differentiation, and integration is just guessing.

换言之,你的任务是要猜出一个二阶导数为a的函数,这就是积分,和微分恰恰相反,积分就是猜

耶鲁公开课 - 基础物理课程节选