If dX/dt is its derivative with respect to time of some object, how would you find the position function of the object?
You would first have to integrate the derivative. We would additionally need more information about the starting position of the object in order to solve for the constant that arrives as a result of integration.
Is it always better to have a higher confidence interval?
No, the size of the confidence interval desired for a problem can change. A higher confidence interval results in the interval being larger and thus less specific.
The natural temperature of the human body is about 98.1 degrees Fahrenheit. If the temperature outside is 98.1 degrees, does that mean you are in equilibrium with your surroundings?
No, as a living being, your body is constantly generating heat from your natural bodily processes. This means that there is a temperature gradient between you and your surroundings. In fact, the only time you are at equilibrium with your surroundings is when you are dead.