The area under a definite integral represents the signed area between a curve and the x-axis within a given interval.
To find the area of a definite integral, you need to evaluate the integral over the given interval and take the absolute value.
For example, if you have the integral:
∫[a,b] f(x) dx
where f(x) is a continuous function, [a,b] is the interval, and dx represents the differential element, you can evaluate the integral and take the absolute value to find the area:
Area = |∫[a,b] f(x) dx|
Note that if the integral evaluates to a negative value, taking the absolute value is necessary to obtain the magnitude of the area.
It's important to note that the definite integral calculates the signed area because the integral takes into account both positive and negative areas above and below the x-axis. The area above the x-axis is considered positive, while the area below the x-axis is considered negative.
Area of Definite integration
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