Mathematics

Problem

Suppose

y = f(x)

and

y = g(x)

are two functions whose graphs intersect at three points

(0, 4)

(2, 2)

and

(4, 0)

with

f(x) > g(x)

for

0 < x < 2

and

f(x) < g(x)

for

2 < x < 4

. If

\int_{0}^{4} [f(x) - g(x)] dx = 10

and

\int_{2}^{4} [g(x) - f(x)] dx = 5

, the area between two curves for

0 < x < 2

, is - (A) 5 (B) 10 (C) 15 (D) 20