Integral-Calculator

Step-by-Step Guide to Using the Integral Calculator

Introduction

The Integral Calculator is designed to help you compute both definite and indefinite integrals of simple polynomial functions of the form c * x^p, where c is the coefficient and p is the power of x. This guide will walk you through the process of using the calculator effectively.

Input Fields

The calculator provides several input fields that you need to fill out to perform the calculations. Here’s how to use each field:

• Type of Integral: Select whether you are calculating a “Definite Integral” or an “Indefinite Integral.” This is a required field. Choose the appropriate type from the drop-down menu.
• Lower Bound (a): Enter the lower bound of the integral if you are performing a definite integral. This field is optional and is ignored for indefinite integrals. Ensure the number you enter matches the required format (any step size is allowed).
• Upper Bound (b): Enter the upper bound in the same conditions as the lower bound. This is also optional and only necessary for definite integrals.
• Coefficient: Enter the coefficient of the polynomial. This is a required field, so ensure you enter a valid number.
• Power of x: Enter the power to which x is raised. It is essential to fill in this field to allow the calculator to compute correctly.

Result Fields

Once you have filled in the input fields correctly, the calculator will display results in the following fields:

• Antiderivative: If you selected “Indefinite Integral,” this field will display the antiderivative of your function in the form coefficient / (power + 1) * x^(power + 1). The output will be displayed with two decimal places.
• Definite Integral Result: For a “Definite Integral,” this field calculates the value using the formula (coefficient / (power + 1)) * (upperBound^(power + 1) – lowerBound^(power + 1)). Results are displayed to four decimal places.
• Area Under Curve: The absolute value of the definite integral result is displayed here, representing the area under the curve. It is displayed with a suffix “square units” and up to four decimal places.

Conclusion

By following these steps and carefully filling out the required fields, you can easily compute integrals using this calculator. Whether finding an antiderivative or calculating the exact area under a curve, the Integral Calculator will provide accurate results based on your inputs.