# What is meant by the area under a curve?

Sep 13, 2015

See the explanation.

#### Explanation:

We say "the area under a curve", but we mean:

On the rectangular coordinate system, we mean the area under a curve and above the $x$-axis between two value of $x$. (And sometimes, "from one value of $x$ to another").

Here is a picture of the are under $y = {x}^{2}$ from $1$ to $3$.

There are variations and complications when speaking to someone in Calculus.

(For example, people sometimes use "the area under the curve" to indicate the NEGATIVE of the area here: