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Absolute value in definite integrals

Exploring absolute value in integrals

Type functions and limits of integration in the corresponding input boxes and click on the check boxes to visualize the corresponding integrals; try for instance a) , b) and c) in the interval from to .
Distinguish between the absolute value of the definite integral of a function and the definite integral of the absulute value of a function, in which cases are the values of these two integrals equal?, which of the integrals will always calculate correctly the area enclosed by a curve and the axis?