Find the area of the shaded region.

The *x* *y*-coordinate
plane is given. There is a curve, two lines, and a region on the
graph.

- The curve
labeled
*y*=*x*^{2}enters the window in the second quadrant, goes down and right becoming less steep, passes through the point (−2, 4) crossing the first line, changes direction at the origin, goes up and right becoming more steep, passes through the point (2, 4) crossing the second line, and exits the window in the first quadrant. - The first line labeled 3
= 2*y*+ 16 enters the window in the second quadrant, goes up and right, passes through the point (−2, 4) crossing the curve, crosses the*x**y*-axis at approximately*y*= 5.3, passes through the point (1, 6) crossing the second line, and exits the window in the first quadrant. - The second line labeled
*y*= 8 − 2enters the window in the second quadrant, goes down and right, crosses the*x**y*-axis at*y*= 8, passes through the point (1, 6) crossing the first line, passes through the point (2, 4) crossing the curve, crosses the*x*-axis at*x*= 4, and exits the window in the fourth quadrant. - The region is above the curve and below the two lines.

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Sol:-The region above the curve y=x^(2) and below the two lines is shaded regionArea of the shaded region is{:[A=int_(-2)^(1)[(1)/(3)(2x+16)-x^(2)]dx+int_(1)^(2)((8-2x)-x^(2))dx],[ ... See the full answer