Question #8e5b5

1 Answer
Sep 12, 2015

Answer:

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:

enter image source here

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.