Question

Question #46fb2

Answer 1

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.