This concept extends the area-between-curves technique to the case where the bounding interval is not given and must first be determined by finding the intersection points of the two curves, requiring the solution of a polynomial equation formed by setting the curves equal. It relies on the definite-integral definition of area between curves (the integral of the upper function minus the lower function over the interval between consecutive intersections) and on polynomial root-finding techniques (recognizing an integer root, then factoring via polynomial division) to establish the bounds. This belongs to single-variable calculus, within the theory of applications of the definite integral, combining that theory with algebraic polynomial-solving as a prerequisite step.
This concept extends the area-between-curves technique to the case where the bounding interval is not given and must first be determined by finding the intersection points of the two curves, requirin…