Answer:
Rounding it to two decimal places, we get distance,
Step-by-step explanation:
Given:
The two points are
The distance between the two points can be obtained using the distance formula which is given as:
Here, for the points,
Therefore, the distance between the points is:
Rounding it to two decimal places, we get
Split up the interval [0, 2] into <em>n</em> equally spaced subintervals:
Let's use the right endpoints as our sampling points; they are given by the arithmetic sequence,
where . Each interval has length
.
At these sampling points, the function takes on values of
We approximate the integral with the Riemann sum:
Recall that
so that the sum reduces to
Take the limit as <em>n</em> approaches infinity, and the Riemann sum converges to the value of the integral:
Just to check: