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Simple integration is a mathematical technique used to find the area under a curve. It involves finding the antiderivative of a function and evaluating it at two points to find the area between those points and the x-axis.
Simple integration is important because it allows us to find the area under a curve, which has many practical applications in fields such as physics, engineering, and economics. It also helps us solve problems involving rates of change and accumulation.
To perform simple integration, you first need to find the antiderivative of the function you are integrating. Then, evaluate the antiderivative at the upper and lower limits of integration and take the difference between the two values.
The main difference between simple integration and definite integration is that in simple integration, the limits of integration are not specified, while in definite integration, the limits are specified. Definite integration also gives a specific numerical value for the area under the curve, while simple integration gives a general expression.
Some common techniques used in simple integration include the power rule, substitution, and integration by parts. These techniques allow us to integrate a wide variety of functions by breaking them down into simpler components and applying specific rules and formulas.
