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English
In mathematics, the term integration has two main meanings. First, it refers to the opposite of differentiation. Differentiation is the process of finding the derivative of a function, which is the measure of how much the function's output changes as its input changes. Integration, on the other handاقرأ المزيد
In mathematics, the term integration has two main meanings.
First, it refers to the opposite of differentiation. Differentiation is the process of finding the derivative of a function, which is the measure of how much the function’s output changes as its input changes. Integration, on the other hand, is the process of finding the antiderivative of a function, which is the function whose derivative is the original function. In other words, integration is the process of “adding up” the derivatives of a function to get the original function.
Second, integration can also refer to the sum of infinitely many small pieces. This is called a definite integral, and it is often used to find the area under a curve. For example, if we want to find the area under the curve of the function f(x) between x = a and x = b, we can use the definite integral:
This integral represents the sum of the infinitely many small rectangles that lie under the curve between x = a and x = b. The width of each rectangle is dx, and the height of each rectangle is f(x).
Integration is a powerful tool for solving problems in mathematics, physics, engineering, and other fields. It is used to find the area under a curve, the volume of a solid, the length of an arc, and many other things.
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