SOLUTION: why do we go for integration and differentiation ?where is it used?

Question 579349: why do we go for integration and differentiation ?where is it used?
Answer by KMST(5347) (Show Source): You can put this solution on YOUR website!
We use differentiation to calculate the rate of change. It is constant for linear functions, being the slope of the line. For nonlinear functions, the derivative function is the slope of the tangent to the graph of the function at that point. It is the "instantaneous" rate of change. It is used a lot in physics, but we also care about it for issues such as rate of exponential grow, rate of exponential decay, rate of reactions. There are uses for derivatives, like differential equations and series expansions that I cannot quite explain.
Integration is also used a lot in physics, to calculate actual value of something as a function of time, when we just know the rate of change. In geometry, it is used to calculate areas and volumes. In chemistry and pharmacology, we calculate area under the curve a lot. (In reality, software programs do it for us, and we may not be able to do it otherwise).
Calculus is useful to understanding new problems, and makes calculations and explanations easier. However, contrary to popular belief, you can learn physics and derive the formulas without resorting to calculus. It is just more work, but where I once lived, all 9th graders were taught physics without calculus (they were just learning trigonometry at the time).
Last time I used integration, I was calculating the volume of a hopper with rectangular openings at the top and bottom connected by flat metal plates. It was not a truncated pyramid, and to calculate it just using geometry required, splitting that solid into other shapes. Using calculus was a much easier and faster way to the answer. As I was solving the problem for people who did not remember calculus, I still had to explain it the long geometry way. However, having the calculus answer allowed me to check for mistakes in the more complicated geometry calculations.
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