Partial Integral Calculator

How to Use the Partial Integral Calculator

The Partial Integral Calculator is an online tool designed to compute the antiderivative and the definite integral of various types of functions. Follow this step-by-step guide to utilize the calculator effectively.

Step 1: Select the Function Type

Begin by specifying the type of function you wish to integrate. The supported function types include:

• Polynomial (ax^n): Select this for any polynomial functions.
• Exponential (e^x): Choose this option for exponential functions.
• Trigonometric (sin x, cos x): Use this for trigonometric functions.

Step 2: Enter Function Parameters

After selecting the function type, provide the necessary parameters:

• Coefficient (a): Enter the coefficient of the function. It must be a number between -1000 and 1000, with steps of 0.1.
• Exponent (n): If you chose a polynomial, specify the exponent here. Valid values range from -10 to 10, with steps of 1.

Step 3: Define the Integration Bounds

Next, input the lower and upper bounds for the integral:

• Lower Bound (a): Specify the lower boundary for the integration. This value should be between -100 and 100, with steps of 0.1.
• Upper Bound (b): Set the upper boundary for the integration, adhering to the same constraints as the lower bound.

Step 4: Calculate the Results

With all inputs provided, the calculator will automatically compute the following:

• Antiderivative: The calculator displays the antiderivative of the chosen function type.
• Definite Integral Result: This value represents the computed definite integral over the specified bounds, presented with four decimal places.
• Area Under Curve: The absolute value of the definite integral gives the area under the curve, measured in square units, displayed also with four decimal precision.

Step 5: Review the Outputs

Examine the results thoroughly to ensure they meet your expected outcomes. The antiderivative formula and the numerical results for the definite integral and the area will help in analyzing the function behavior over the specified range.

By following these steps, you can effectively utilize the Partial Integral Calculator to obtain the necessary calculus computations for your selected function type.