You mean besides finding the exact are under the curve of y=x^2?!?! Haha.
How about driving a car? The integral of acceleration over a given time interval will yield the final velocity.
Well, I saw this awesome demonstration of the mean-value theorem for applied purposes in a calculus book.Originally Posted by m777
A man is driving at a certain speed in his car. There are two police officers (fat ones eating donuts) at exit 10 and exit 11. The man has a sensor and knows where these officers are hiding. When he approaches exit 10 he slows down to 60 miles per hour. Further when he approaches exit 11 after 40 seconds he slows down to 55 miles per hour. The man is later fined for speeding! Why? Because these fat police officers were calculus experts (how many fat people do you know who are calculus experts? I know at least one). They used the mean value theorem. They deduced the mean speed between exit 10 and exit 11 (which had 1 mile distance). And knew that there had to be an instant when this man had this mean speed (instantenous speed = derivative) by the mean value theorem which was above 65 miles and fined him
I don't think that you are doing justice with the role of the integration(and calculus) in our daily lives.
What is the use of water in our daily lives? You could list a few common uses. Apart from that there are numerous indirect uses without which our life would be miserable.
Integration may have very limited use directly in our daily lives, but it is very important.I would rephrase your question as"how would you compare the daily life of today with the one in which integration is not known.?"
Electricity may be discovered without integration but inductors, capacitors cannot be used without it. You are using mobile conection, which is due to the excellent work of satellies in space.But can the satellites be put into space without the use of integration?