Can anybody say me what is differentiation and integration and what is the use of these ?
closed as off-topic by Amy B, Chris Cunningham♦, Joel Reyes Noche, Tommi Brander, Wrzlprmft Jul 1 '18 at 8:13
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If you've traveled in an automobile, you've experienced both the integral and derivative viscerally. Stepping on the gas pedal accelerates your speed and pushes you back into the seat cushion. This acceleration is the derivative of your velocity. When you brake, your speed decreases, the derivative is negative, and you are pulled forward in your seat.
Traveling 60 km/hr for an hour moves the car 60 km of course. This distance traveled is the integral of your velocity. The same works when your speed varies over time: the distance covered is the integral of the time-varying velocity with respect to time.
Differentiation has to do with rates. (What your car's value will be in a few years, how much money you'll have in a bank account with interest rates, how long will it take for your garden's carrots to be ripe, determining hunting quotas (in order to let preys reproduce enough), etc.)
Integration has to do with adding multiple small pieces to know more about the whole. For example, you can figure out volumes and areas of almost anything you want using integration. It has many applications in physics for example (as shown by Jospeh O'Rourke's example).
I would argue that integration, unlike differentiation, doesn't really have many direct ways in which it can be used in every day life. That being said, there are many things you do use in every day life that couldn't exist if integration (and calculus in general) was not developed (cellphones, computers, engines, etc.).