# Question #8e5b5

Sep 12, 2015

We are trying to find the area under a curve.

#### Explanation:

Suppose we have a function $f \left(x\right) = 2 x$:

graph{2x [-10, 10, -5, 5]}

The integral from measures the area between this curve and the $x$-axis.

For instance, the integral from 0 to 1 tells us how big the following space is:

When we say "integral from 0 to 1" we mean look at the curve between where $x = 0$ and $x = 1$.

In this case, when $x = 0$, $y = 0$, and when $x = 1$, $y = 2$. So the space between the curve and the $x$-axis is a triangle with base 1 and height 2, so the area and the integral both equal 1.