line: y = -1/2x + 4 area: is 7/3 you'll have to find the slope of the tangent line first which is: y' = 2x - 2 = 2(2) - 2 = 2 the perpendicular slope is then -1/2 y - 3 = -1/2(x - 2) y = -1/2x + 4
then you integrate, by using the line as the upper area, then subtracting the lower area parabola between 0 and 2 int(-1/2x + 4 - (x^2 - 2x + 3)) = -1/4x^2 + 4x -x^3/3 + x^2 - 3x replace 2 for x and you will get -1 + 8 - 8/3 + 4 - 6 12 - 29/3 = 7/3
