Riemann Sum Calculator

How to Use the Riemann Sum Calculator

Step 1: Select the Function

Begin by choosing the function you wish to integrate from the available options. Click on the dropdown menu labeled Select Function. You will see a list of functions such as x², x³, sin(x), cos(x), and e^x. Select the function you want to work with by clicking on it.

Step 2: Enter the Lower Bound

Next, you will need to specify the lower bound of the interval over which you will approximate the integral. In the field labeled Lower Bound (a), enter a number between -100 and 100. This field is indicated as required, which means you cannot leave it empty. Make sure to enter a valid number using increments of 0.1.

Step 3: Enter the Upper Bound

The upper bound is the next value that you will input. In the field labeled Upper Bound (b), enter a value that is also between -100 and 100. This value represents the endpoint of the interval. Ensure your upper bound is greater than the lower bound to define a valid interval.

Step 4: Input the Number of Rectangles

You must decide the number of rectangles (n) to use in your approximation. This is entered in the field labeled Number of Rectangles (n). Enter a whole number between 1 and 1000. The more rectangles you choose, the more accurate the approximation will be.

Step 5: Choose the Approximation Method

Now, select the method used for the approximation by clicking the dropdown menu labeled Approximation Method. You have the option to choose between Left Endpoint, Right Endpoint, and Midpoint. Each method involves a different approach in calculating the Riemann sum, so choose according to your preference or requirement.

Step 6: View the Results

Once you’ve completed the input fields, the calculator will automatically compute and display the results. The Width of Each Rectangle (Δx) shows the width of each rectangle used in the approximation based on your input bounds and number of rectangles.

The Riemann Sum displays the estimated integral of the function over the specified interval using your chosen method.

Finally, view the Error Estimate to understand the difference between the calculated Riemann sum and the actual integral. This value indicates the accuracy of the approximation.