Improper Integral Calculator

Guide to Using the Improper Integral Calculator

Understanding the Purpose

The Improper Integral Calculator is designed to assist with evaluating integrals that have either infinite limits, or which involve integrals of functions with asymptotes within the interval of integration. This guide will walk you through using the calculator efficiently.

Preparation

Before you begin, ensure that you have a clear understanding of the integral you wish to evaluate, including its limits and the nature of the function (the integrand).

Step 1: Configuring the Limits

• Lower Limit: Select the nature of the lower limit from the provided options. Choose between “Negative Infinity (-∞)” or “Finite Value”.
• If “Finite Value” is selected, an additional field titled Lower Limit Value will appear. Enter the specific numerical value of the lower limit in this field.

• Upper Limit: Similarly, choose between “Positive Infinity (∞)” or “Finite Value” for the upper limit.
• If “Finite Value” is chosen, you will be prompted to fill in the Upper Limit Value, by providing the appropriate numerical value.

Step 2: Selecting the Integrand Type

• Integrand Type: Select the type of function being integrated. Options available are “Exponential (e^x)”, “Rational (1/x^n)”, and “Trigonometric”. This selection will determine which fields need to be completed in the following steps.

Step 3: Entering Coefficient and Exponent

• Coefficient: Enter the coefficient of the integrand. Ensure this value is between -1000 and 1000, as per the validation constraints.
• Exponent (for rational functions): If your integrand type is “Rational”, you will need to enter an exponent value. This must be a non-negative integer of up to 10.

Step 4: Reviewing the Results

• Convergence Status: After computation, check the convergence status to determine whether the integral converges.
• Integral Value: The calculator provides the approximate value of the improper integral, formatted to four decimal places.
• Interval of Convergence: If applicable, review the interval over which the selected function converges.

Once all fields are filled, the calculator performs the necessary calculations and displays the results. Ensure that the input data is accurate to obtain a reliable evaluation of the improper integral.