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Area Between a Curve and the X Axis
To find the area between a curve and the x-axis, the most preferred tool is definite integration of the given curve.
To find the area under the curve y = f(x) between x = a and x = b, integrate y = f(x) between the limits of a and b.
Some Examples
NOTE: Areas under the x-axis will come out negative and areas above the x-axis will be positive. This means that you have to be careful when finding an area which is partly above and partly below the x-axis.