What the difference between derivative and integration
Derivative and integration are two fundamental concepts in calculus, and they are inverse operations of each other. The key difference between these two concepts is that derivative quantifies the rate of change or slope of a function at a particular point, whereas integration gives the area under a curve between two points.
In other words, derivative calculates the rate of change of a function, while integration calculates the accumulated value of a function over a given period, and these two operations are interconnected. The derivative of a function gives the slope of the tangent line at any point on the function, while integration gives the area between the function and the x-axis between two points.
Another way to understand the difference between derivative and integration is to think of them as forwards and backward operations, respectively. Derivatives take a function and calculate its rate of change, while integrals take a rate of change (i.e., a derivative) and calculate the original function.
In summary, derivatives and integrals are two essential and interconnected concepts in calculus that are used to solve real-world problems in physics, engineering, economics, and many other fields.