Integration Calculator

The Integration Calculator helps users compute the definite integral, area under the curve, and mean value for polynomial, trigonometric, and exponential functions within specified bounds.

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How to Use the Integration Calculator

This guide will walk you through the steps required to use the Integration Calculator effectively. By following these steps, you can calculate the definite integral, area under the curve, and the mean value of a given function.

Step 1: Select Function Type

  • Begin by choosing the type of function you are working with.
  • You will find a dropdown labeled Function Type with the following options:
    • Polynomial Function
    • Trigonometric Function
    • Exponential Function
  • Ensure you select the function type that corresponds to your problem.

Step 2: Enter the Lower Bound and Upper Bound

  • Locate the input field labeled Lower Bound (a) and enter the value of the lower bound of integration. This value should be between -1000 and 1000 and can include decimals.
  • Next, enter the upper bound in the Upper Bound (b) field with the same value requirements as the lower bound.

Step 3: Enter the Coefficient

  • Insert the coefficient of your function in the Coefficient field.
  • Ensure this value is between -100 and 100, allowing for decimals.

Step 4: Enter the Power (For Polynomial Functions Only)

  • If you selected Polynomial Function in Step 1, you need to specify the power of the polynomial.
  • Enter this integer value in the Power (for polynomial) field, ensuring it is between 0 and 10.

Step 5: Calculate the Results

  • After entering all necessary inputs, the calculator will automatically compute the following results:
    • Definite Integral Result: The result calculated based on the input values and function type.
    • Area Under Curve: Displays the absolute value of the definite integral, shown with the unit in square units.
    • Mean Value of Function: The average value of the function over the interval, calculated as the definite integral divided by the difference between the upper and lower bounds.
  • Results for each will be displayed with precision up to four decimal places.

By following these steps, you can leverage the Integration Calculator to find various integral properties of different types of functions effectively.