Question #46fb2

1 Answer
Nov 18, 2017

The area is 1/12 square units.

Explanation:

The area beneath the f(x) curve from 0 to 1 can be represented as:
10x2dx

The anti-derivative of this integral is (13)(x3).

Thus the integral can be written as (13)(13)(13)(03), which equals (1/3). The area between the f(x) curve and the x axis is 13 square units.

Do the same thing for g(x).
10x3dx

Anti-derivative is (14)(x4).

(14)(14)(14)(04)=14

Since you want to find the area between f(x) and g(x) from the interval (0,1), simply subtract the two values.

1314=112

The area is 1/12 square units.