Help! calculus and tangent question? (1 Viewer)

[fabl]

A function y = 12x-32-x^2 has x intercepts of 4 and 8. A tangent to this curve has equation of y=2x-7 at point A where x =5.

If the tangent meets the x axis at B, and C is the x intercept of the parabola closer to the origin, find the area of the region bounded by AB, BC and arc CA?

The answer is 7/12 unit squared. Do not know what steps to take to achieve this? I tried dif integration

 

[swagswagyoloswag]

When you draw it up it will consist of a concave down parabola cutting at 4 and 8.there will also be a line that is tangent at x = 5 and bounds the area together with the parabola. This area would be area under the line from the x intercept of the line (x = 3.5) and to x = 5 - area under parabola from x= 4 to x=5.This is represented as