Consider the functions and

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Consider the functions

f(x)

and

g(x)

, both defined from

\mathbb{R}\to\mathbb{R}

and are defined as

f(x) = 2x - x^2

and

g(x) = x^n

where

n \in \mathbb{N}

. If the area between

f(x)

and

g(x)

1/2

, then

n

is a divisor of (1) 12 (2) 15 (3) 20 (4) 30