Question

Question #8e5b5

Answer 1

We are trying to find the area under a curve.

Explanation:

Suppose we have a function `f(x) = 2x`:

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.