Use a Riemann sum with four subintervals of equal length (n = 4) to approximate the area of R. Choose the representative points to be the left endpoints of the subintervals.

Answer 1

Riemann sum is a method of calculating the area under a curve by breaking the curve up into separate blocks. Using the left endpoint means the height of each block is determined by the function's value at the left end point.

Since there are four subintervals, we find the width of each block using the following equation:

width=length/number of intervals = 4/4 = 1

So our width is 1.

Now, we can plug into our equation. Since we are not given the equation or a picture, I will type it out in terms of n.

Area = width * [f(x) + f(x + width) + ... ] = 1 * [f(0) + f(1) + f(2) + f(3)] where f(0) is the first point at the start of the interval, f(1) is one unit further, etc.

Hope this helps!