Hi,i get confuse in the term of derivative and integration. as this topic studied in college but cant relate with real life.
means where this terms actually use.
Well, I wish someone explained it to me like you did, when I was on my first courses. Totally agree with that.The simplest usage of derivative and integration is in their application to speed (velocity) and distance traveled.
derivative = differentiation = difference = change
If a car's speed changes from 60mph to 62mph in 1 second, the change is 2mph per second. This is the derivative of the speed. The car is accelerating at 2mph/s.
integration = integral = total = sum
If we were to record the speed of the car at each second, how far does the car travel from time 20 second to time 22 second? We integrate.
Suppose the speed of the car is steady at 60mph.
60mph = 88 feet per second.
The car travels 88 feet in the first second and 88 feet in the second second.
Total distance traveled in the 2-second interval is 176 feet.
What happens if the car is accelerating from 60mph to 62mph during the 2-second interval?
What is the distance traveled during that 2-second interval?
To keep the calculation simple,
suppose in the first second the average speed is 88 feet per second. Distance traveled is 88 feet.
Suppose in the second second the average speed is 90.9 feet per second. Distance traveled is 90.9 feet.
To find distance traveled we integrate the speed over the duration of interest.
Distance traveled is 88 + 90.9 = 178.9 feet.
In summary,
integration = sum
derivative = difference