What is differentiation and integration
What is differentiation and integration
DIFFERENTIATION:
Differentiating a function gives its rate of change. As the rate of change varies, it gives a new function. For example, differentiating your position as a function of time gives the velocity, and differentiating your velocity as a function of time gives your acceleration.) In general these are vector functions, but if you are moving along a straight line, they are scalar functions.)
INTEGRATION:
Integration is the reverse process of differentiation, for example you get your velocity by integrating your acceleration and you get you position by integrating your velocity. There’s another way to look at integration. You are approximately adding small changes. If your acceleration is constant, the increase in your velocity is just the acceleration multiplied by the time. But if the acceleration varies it doesn’t change much over a few milliseconds (or microseconds) so you can multiply it by that short time interval and add similar results for other time intervals. This would give your approximate change in velocity. But the shorter the little time intervals you add, the better the approximation. The integral is the limiting value of these approximations as the time intervals approach zero.
I used functions of time as examples. In general you could use functions of anything you like. For example the volume of a sphere is the integral of the surface area with respect to the radius.
DIFFERENTIATION:
Differentiating a function gives its rate of change. As the rate of change varies, it gives a new function. For example, differentiating your position as a function of time gives the velocity, and differentiating your velocity as a function of time gives your acceleration.) In general these are vector functions, but if you are moving along a straight line, they are scalar functions.)
INTEGRATION:
Integration is the reverse process of differentiation, for example you get your velocity by integrating your acceleration and you get you position by integrating your velocity. There’s another way to look at integration. You are approximately adding small changes. If your acceleration is constant, the increase in your velocity is just the acceleration multiplied by the time. But if the acceleration varies it doesn’t change much over a few milliseconds (or microseconds) so you can multiply it by that short time interval and add similar results for other time intervals. This would give your approximate change in velocity. But the shorter the little time intervals you add, the better the approximation. The integral is the limiting value of these approximations as the time intervals approach zero.
I used functions of time as examples. In general you could use functions of anything you like. For example the volume of a sphere is the integral of the surface area with respect to the radius.
