Question

what is formula for left riemann sum

Answer 1

$$S = \sum_{i=1}^{n} f(x_i) \cdot (x_i -x_{i-1})$$

Answer 2

Which can also be written as:
$$S = \sum_{i=1}^{n} f(x_i) \cdot \varDelta x$$

Answer 3

You're getting to the point in your math career where "formulas" are less helpful than "concepts". Understanding certain things allows you to create the formula with almost no effort.

For instance, how do you find the area of a right triangle? Do you use A=1/2*b*h or are you able to think, well, a rectangle has an area of length times width, and if I cut it in half with a diagonal line, I make two of the same triangle, so half of that must be the area I'm looking for.

See, memorizing formulas can fail you on the test. Reasoning things out allows you to just figure out almost anything.

For instance, what's this Left or Right riemann sum stuff? It's just looking at a function at only points that are equally spaced from each other. Then we see that on the curve we have two different places we can use an approximation of the height, the point on the left or the right. Then we just find the area of each one, since they're at regular intervals they all have the same width.

Answer 4

↑ "You're getting to the point in your math career where "formulas" are less helpful than "concepts"." 110% agreed.