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1.9.22: Anti-derivatives
https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_I_(2211)/01%3A_Introduction_to_Physics_Measurements_and_Mathematics_Tools/1.09%3A_Math_Review_of_Other_Topics/1.9.22%3A_Anti-derivatives
Therefore, every antiderivative of $\cos x$ is of the form $\sin x+C$ for some constant $C$ and every function of the form $\sin x+C$ is an antiderivative of $\cos x$ . Therefore, every antid...Therefore, every antiderivative of $\cos x$ is of the form $\sin x+C$ for some constant $C$ and every function of the form $\sin x+C$ is an antiderivative of $\cos x$ . Therefore, every antiderivative of $e^x$ is of the form $e^x+C$ for some constant $C$ and every function of the form $e^x+C$ is an antiderivative of $e^x$ .
4.7: Looking Back and Ahead
https://phys.libretexts.org/Under_Construction/Purgatory/4%3A_Models_of_Thermodynamics/4.7%3A_Looking_Back_and_Ahead
It is because we always deal with systems in everyday experience that have 1020 or more particles, that we can make absolute statements like, “heat always flows from a hotter object to a cooler object...It is because we always deal with systems in everyday experience that have 1020 or more particles, that we can make absolute statements like, “heat always flows from a hotter object to a cooler object.” It is not that some fundamental law of physics would be violated (conservation of energy, for example) if we sometimes ran across an interaction in which energy was transferred from the cooler to the warmer system as heat.
1.9.22: Anti-derivatives
https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Physics_II_(2212)/01%3A_Introduction_to_Physics_Measurements_and_Mathematics_Tools/1.09%3A_Math_Review_of_Other_Topics/1.9.22%3A_Anti-derivatives
Therefore, every antiderivative of $\cos x$ is of the form $\sin x+C$ for some constant $C$ and every function of the form $\sin x+C$ is an antiderivative of $\cos x$ . Therefore, every antid...Therefore, every antiderivative of $\cos x$ is of the form $\sin x+C$ for some constant $C$ and every function of the form $\sin x+C$ is an antiderivative of $\cos x$ . Therefore, every antiderivative of $e^x$ is of the form $e^x+C$ for some constant $C$ and every function of the form $e^x+C$ is an antiderivative of $e^x$ .

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