MATH
posted by AIRA .
Region A that on xyplane is bounded by two (2) curves and a line. The curves are y=x^32x+3 and y=x^2+3 while the line is x=0. It is located in the first quadrant of xyplane. Determine the area of region A.

Make a sketch and then solve for the intersection of the two curves
x^2  2x + 3 = x^2 + 3
.....
x = 0 or x = 1
so
area = [integral] (x^2 + 3 (x^2  2x+3)) dx from 0 to 1
= integral (2x^2 + 2x)dx from 0 to 1
= (2/3)x^3 + x^2  from 0 to 1
= 2/3 + 1  0
= 1/3