Find the area of the region

Question

y = x² − 3x,  y = 3x + 7

Find the area of the region: ________

Answer 1

x^2 - 3x = 3x+7

x^2 - 6x - 7 = 0

(x - 7)(x + 1 ) = 0

they intersect at (7,28) and (-1,4)

the linear function is on top

3x+7 - x^2 -3x = 7-x^2 integrates to 7x - (1/3)x^3

as x-->-1 the limit is -7 + 1/3 = -20/3

as x--> 7 the limit is -196/3

subtracting: -173/3