Iterated Integral Calculator

The Iterated Integral Calculator allows users to compute double integrals with customizable limits and integrand types, providing results for inner and outer integrals as well as the area under the surface.

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How to Use the Iterated Integral Calculator

This step-by-step guide will walk you through using the Iterated Integral Calculator to compute double integrals with specified limits and integrands. Follow each step carefully to obtain accurate results.

Step 1: Enter Outer Limits for Integration

  • Outer Lower Limit: Enter the lower limit for your outer integral in the input field labeled “Outer Lower Limit.” This value is required to proceed with the calculation.
  • Outer Upper Limit: Similarly, enter the upper limit for your outer integral in the “Outer Upper Limit” field. Ensure this value is also provided as it is necessary for the integration process.

Step 2: Enter Inner Limits for Integration

  • Inner Lower Limit: Input the lower limit for your inner integral in the “Inner Lower Limit” field. This field is essential and must be filled.
  • Inner Upper Limit: Add the upper limit for your inner integral in the “Inner Upper Limit” field, keeping in mind that this is a mandatory input for accurate calculations.

Step 3: Select Integrand Type

  • Integrand Type: Use the dropdown menu in the “Integrand Type” field to select the type of integrand you wish to work with. Options include:
    • Polynomial (e.g., xn)
    • Exponential (e.g., ex)
    • Trigonometric (e.g., sin(x), cos(x))

Step 4: Enter Coefficient and Exponent (if applicable)

  • Coefficient: Provide the coefficient value needed for your integrand. This must be a number between -1000 and 1000, and is a required field.
  • Exponent: If you have selected a polynomial integrand, input the exponent value in the “Exponent (for polynomial)” field. Although optional, it should be a number between 0 and 10 if a polynomial is chosen.

Step 5: Calculate the Result

After entering all necessary fields, the calculator will automatically compute the results. The following details will be provided:

  • Inner Integral Result: Displays the result of the inner integral calculation, formatted to four decimal places.
  • Final Double Integral Result: This gives you the result of the full iterated double integral, again with four decimal precision.
  • Area Under Surface: This field shows the absolute value of the outer integral, representing the area under the surface, expressed in square units and displayed with four decimal accuracy.

By carefully following these steps, you can effectively utilize the Iterated Integral Calculator for your mathematical needs.