AP Calculus AB and BC glossary
Net signed area
A definite integral computes net signed area, counting regions above the x-axis as positive and regions below as negative. That is why an integral can come out zero or negative even though geometric area never can.
To get true geometric area instead, integrate the absolute value of the function, or split at the zeros and add the absolute values of the pieces. That is the same distinction as displacement against total distance.
The mistake
Answering an area question with a negative number. If the result is negative you computed net signed area, and the question wanted the absolute version.
Appears in: Unit 6: Integration and Accumulation, Unit 8: Applications of Integration