Find the area of the region bounded by and the lines

MATHEMATICS · Subjective · A Level · Mathematics · Integration · Integration

Problem

Find the area of the region bounded by

y = f(x), y = |g(x)|

and the lines

x = 0, x = 2

, where

f, g

are continuous functions satisfying

f(x+y) = f(x) + f(y) - 8xy, \forall x, y \in \mathbb{R}

and

g(x+y) = g(x) + g(y) + 3xy(x+y), \forall x, y \in \mathbb{R}

Also,

f'(0) = 8

and

g'(0) = -4