Question

How do you find the area under the curve `f(x)=x^2` on the interval [-1,1]?

Answer 1

`A = 2/3` units squared

Explanation:

Area under a curve on an interval is analogous to the integral of the function of the curve on an interval.

`A = \int_(x_i)^(x_f)f(x)dx`

`= \int_(-1)^(1) x^2 dx`

`=[x^3/3]_(x=-1)^(x=1)`

`=1/3 - (-1/3) = 2/3` units squared