Integral Calculator

The Integral Calculator helps users compute the definite integral of a given mathematical function, providing results such as the integral value, antiderivative formula, and the area under the curve.

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How to Use the Integral Calculator

This guide will walk you through the steps required to calculate the integral of a given function using the Integral Calculator. Follow each step carefully to ensure accurate results.

Step 1: Enter the Lower Bound

Begin by entering the lower bound, denoted as a, in the field labeled Lower Bound (a). This value represents the starting point of the interval over which you want to calculate the integral. Make sure this field is filled as it is required for the calculation.

Step 2: Enter the Upper Bound

Next, fill in the upper bound, denoted as b, in the field labeled Upper Bound (b). This is the endpoint of the interval. Like the lower bound, this field is also required to proceed with the calculation.

Step 3: Select the Function Type

Choose the type of mathematical function for your integral using the Function Type dropdown menu. The available options are:

  • Polynomial (x^n)
  • Exponential (e^x)
  • Trigonometric (sin x, cos x)
  • Logarithmic (ln x)

This selection is mandatory and will determine the form of the function you want to integrate.

Step 4: Enter Coefficient

Provide the coefficient for the function in the field labeled Coefficient. This value will be multiplied by the function type you have selected. The coefficient is necessary for accurate computation.

Step 5: Specify the Power (For Polynomial)

If you selected Polynomial (x^n) as the function type, enter the power of x in the Power (for polynomial) field. Ensure this value is non-negative as required by the validation rules.

Step 6: View the Results

After providing all the necessary information, the calculator will compute the following outcomes:

  • Definite Integral Result: This value represents the integral of the function from a to b. The result is formatted to four decimal places.
  • Antiderivative Formula: You will see the formula for the antiderivative of the function, formatted to two decimal places. This representation includes the power incremented by one.
  • Area Under Curve: Displays the absolute value of the definite integral, indicating the area under the curve. The result is given in units squared, formatted to four decimal places.

By following these steps, you can efficiently calculate the integral of a specified function using the Integral Calculator.