Question

Which definite integral approximation formula is the integral from a to b of f of x, dx is approximately equal to the product of the quantity b minus a over n and the quantity y sub 0 plus y sub 1 plus y sub 2 plus y sub 3 plus dot dot dot plus y sub n minus 1?

Answer 1

Explanation:

Given that integral approximation formula is calculated as follows:

Integral from a to be of f(x) dx is calculated as dividing the region between the curve, the x axis and y=a and y=b into a number of trapeziums (n) of equal width and then calculating the area of the trapeziums and adding.

The width of triangle would be (b-a)/n

The length would vary depending on the position of x.

First rectangle has length = y_0 = f(a)

Hence left end points are used

So this is Riemann left sum approximation.

Answer 2

That is a description of the formula for the rectangle rule using left endpoints.