Find the area of the region between the graphs of y = 13 − x 2 and y = − 5 x + 7 over the interval 3 ≤ x ≤ 9 . The area is

Question

Find the area of the region between the graphs of  and  over the interval .The area is  

Answer 1

You need to graph the two curves to have some idea what is happening. You can figure out where the two curves intersect by equating the curves (the quadratic is factorable to (x-6)(x+1) which means that the curves cross at x = 6.

As a result you have to break up the integral of the area into 2 pieces: from 3 to 6 and from 6 to 9.

Area = Int (3 to 6) of (13-x²-(-5x+7))dx + Int(6 to 9) of (-5x+7-(13-x²)dx

(6x-2x³/3-5x²/2) evaluated from 3 to 6 - () evaluated from 6 to 9 (Where the same integral is in the parentheses).