MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
For the two curves y=2x+3 and y=x2, consider the interval x∈[−1,2]. Answer the following:
(i) Sketch the graphs of both curves on the same set of axes and shade the region enclosed between them for the given interval.
(ii) Identify which of the two curves acts as the upper boundary and which as the lower boundary throughout [−1,2], giving suitable justification.
(iii) Write, but do not evaluate, the definite integral that represents the exact area of the shaded region.