Reimann sums approximate the area of an integral using what?
skinny rectangles
see
https://brilliant.org/wiki/riemann-sums/
area under the curve?
Riemann sums approximate the area of an integral using rectangles. To calculate the Riemann sum, you divide the interval over which you want to integrate into smaller subintervals (also known as partitions) and create rectangular approximations for each subinterval.
There are several types of Riemann sums, including left endpoints, right endpoints, midpoint, and Trapezoidal sums. Each type uses a different method to determine the height of the rectangle.
To calculate a Riemann sum, you start by dividing the interval [a, b] into n equally sized subintervals. The width of each subinterval, which is denoted as Δx, is given by (b-a)/n.
Next, you choose a representative point within each subinterval to determine the height of each rectangle. For example, in a left endpoint Riemann sum, you would use the left endpoint of each subinterval as the height. In a right endpoint Riemann sum, you would use the right endpoint of each subinterval. And in a midpoint Riemann sum, you would use the midpoint of each subinterval.
Once you have determined the heights, you multiply each height by the corresponding width to calculate the area of each rectangle. Finally, you sum up the areas of all the rectangles to approximate the area under the curve or the integral.
By increasing the number of subintervals (n) and making them infinitely small, Riemann sums can converge to the exact value of the integral, providing a good approximation of the area under the curve.