Question

Region A that on xy-plane is bounded by two (2) curves and a line. The curves are y=x^3-2x+3 and y=-x^2+3 while the line is x=0. It is located in the first quadrant of xy-plane. Determine the area of region A.

Answer 1

First find the points where the curves intersect. 0 and 1. then take the integral of both from 0 to 1. The difference of the two is the answer.

Answer 2

\[\int\limits_0^1(-x^2+3) dx- \int\limits_0^1(x^3-2 x+3)\]