Final answer:
To approximate the area under a curve using Riemann sums in Desmos, the left and right endpoints, a and b, need to be set using the sliders on rows 7 and 8.
Step-by-step explanation:
The Riemann sums calculator in Desmos can help us approximate the area under the curve of the function f(x) = (x/2)(sin(x²)) + 0.51. To do this, we need to set the left and right endpoints, a and b, using the sliders on rows 7 and 8. Please indicate the values you have chosen for a and b.
Without access to the specific Desmos calculator the student is using, it's not possible to provide specific left and right endpoint values, but the student is advised on how to use the sliders to find the area under the curve using Riemann sums.
To approximate the area under the curve of the function f(x) = (x/2)(sin(x²)) + 0.51 using a Riemann sums calculator in Desmos, you need to select appropriate values for a and b, which are the left and right endpoints respectively. Unfortunately, as a tutor, I do not have access to the Desmos calculator you are using and cannot see the sliders or their value range. Generally, you would move these sliders to cover the interval where you are interested in finding the area under the curve. Once a suitable interval is selected, the Desmos calculator will compute the Riemann sum approximation for that interval.
If you are looking for the total area under the curve for all positive values of x, you might set a to 0 and choose a reasonable upper bound for b. As for getting an accurate approximation, you may need to adjust the number of partitions to ensure that the sum is close to the true value of the integral. The more partitions used, the closer the Riemann sum will be to the actual area.