Double Integral Calculator

Guide to Using the Double Integral Calculator

Step 1: Understanding the Input Fields

Before using the calculator, familiarize yourself with the input fields which are essential for calculating the double integral:

• Upper limit of x: Enter the upper boundary for the variable x. This is a required field.
• Lower limit of x: Define the lower boundary for the variable x. This field is also required.
• Upper limit of y: Set the upper boundary for the variable y. Make sure to fill in this required field.
• Lower limit of y: Provide the lower boundary for the variable y. This is necessary to proceed with the calculation.
• Select Function f(x,y): Choose a function from the available options to be integrated over the defined range. This selection is mandatory.

Step 2: Setting the Limits of Integration

Input the limits for x and y variables:

• Start by entering the Upper limit of x and Lower limit of x. Ensure the lower limit is less than the upper limit to define a valid range.
• Next, input the Upper limit of y and Lower limit of y. Similar to x, make certain that the lower limit is below the upper limit.

Step 3: Selecting the Function

Choose the function that you want to integrate within the specified limits:

• Use the dropdown menu to select one of the predefined functions, such as xy, x² + y², sin(x)cos(y), e^(x+y), or x²y.
• This function choice will dictate the actual calculation of the integral, so select according to your needs.

Step 4: Retrieve and Interpret the Results

Once all input fields are filled correctly, the Double Integral Calculator will provide the following results:

• Double Integral Result: This value represents the evaluated double integral of the chosen function over the specified limits. It is displayed to six decimal places.
• Area of Integration: The calculator will compute the area over which the integration is performed and present it in square units. This value is shown with four decimal places.
• Average Value of Function: By dividing the integral result by the area, the calculator provides the average value of the function across the integration region. This result is accurate to six decimal places.

Review the results to ensure they match the expectations of the calculation based on the input parameters specified.