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:
int_0^1x^2dx

The anti-derivative of this integral is (1/3)(x^3).

Thus the integral can be written as (1/3)(1^3)-(1/3)(0^3), which equals (1/3). The area between the f(x) curve and the x axis is 1/3 square units.

Do the same thing for g(x).
int_0^1x^3dx

Anti-derivative is (1/4)(x^4).

(1/4)(1^4)-(1/4)(0^4) = 1/4

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

1/3-1/4 = 1/12

The area is 1/12 square units.