?Thank you.That meant a lot to me.BvU said:
Integration is a mathematical process that involves finding the area under a curve. It is used to solve problems related to accumulation, such as finding the total distance traveled by an object or the total amount of a substance produced over time.
The two types of integration are definite and indefinite. Definite integration involves finding the exact value of the area under a curve between two given points, while indefinite integration involves finding the general form of the antiderivative of a function.
The fundamental theorem of calculus states that integration and differentiation are inverse operations of each other. This means that if we integrate a function and then differentiate the result, we will get back the original function.
To solve an integration problem, you need to follow a set of steps. First, identify the type of integration (definite or indefinite) and the function to be integrated. Then, use integration rules and techniques, such as substitution or integration by parts, to find the antiderivative. Finally, evaluate the antiderivative at the given limits (for definite integration) or leave it in general form (for indefinite integration).
Integration has many real-world applications, including calculating the area under a velocity-time graph to find the distance traveled by an object, finding the volume of irregular shapes in engineering and architecture, and determining the total revenue or profit of a company over time in economics and business.