Question

Use a calculator to compute the left sum, midpoint sum, and right sum for the function f, using a partition with 30 subintervals of the same length. Give at least 6 decimal places of your calculator answers. Left sum:

a. True
b. False.

Answer 1

To compute left, midpoint, and right sums for a function using a partition with 30 subintervals, you need to evaluate the function at the left, middle, and right endpoints of each subinterval and multiply each value by the width of the subinterval. Add up all these products to find the sum. Use a calculator to perform these computations.

Step-by-step explanation:

To compute the left sum, midpoint sum, and the right sum for a function using a partition with 30 subintervals of the same length, you will need a calculator that allows you to evaluate definite integrals. Here are the steps to compute each sum:

1. Divide the interval over which the function is defined into 30 equal subintervals.
2. Calculate the width of each subinterval by finding the difference between the upper and lower bounds of the interval and dividing it by the number of subintervals.
3. For the left sum, evaluate the function at the left endpoint of each subinterval and multiply it by the width of the subinterval. Add up all these products.
4. For the midpoint sum, evaluate the function at the midpoint of each subinterval and multiply it by the width of the subinterval. Add up all these products.
5. For the right sum, evaluate the function at the right endpoint of each subinterval and multiply it by the width of the subinterval. Add up all these products.

Use a calculator to carry out these computations and provide the answers to each sum.