Line Integral Calculator

Using the Line Integral Calculator

This guide will walk you through the steps of using the Line Integral Calculator to determine the path length, line integral, and work done over a specified path in a vector field.

Step 1: Enter the Starting and Ending Coordinates

Begin by entering the coordinates for the start and end points of the path:

• Starting Point x₁: Input the x-coordinate of the starting point in the designated field. This field is required.
• Starting Point y₁: Input the y-coordinate of the starting point. This field is also required.
• Ending Point x₂: Input the x-coordinate of the ending point. This entry is mandatory.
• Ending Point y₂: Input the y-coordinate of the ending point, which is a required field.

Step 2: Select the Vector Field Type

Choose the type of path for your vector field:

• Linear Path: This option is suitable for paths that follow a straight line.
• Circular Path: Select this for paths that are circular in nature.

Step 3: Enter the Coefficients for M(x,y) and N(x,y)

The calculator requires coefficients for the vector components:

• M(x,y) Coefficient: Enter the coefficient associated with the M component of the vector field. This field must be filled.
• N(x,y) Coefficient: Enter the coefficient for the N component, which is necessary to proceed with the calculation.

Step 4: Calculate the Results

Once all fields are completed, the calculator will compute the following:

• Path Length: Calculated using the formula sqrt((x₂ – x₁)² + (y₂ – y₁)²), and the value is presented with up to four decimal places.
• Line Integral Value: This is derived from the expression M(x,y) coefficient * (x₂ – x₁) + N(x,y) coefficient * (y₂ – y₁), with results given to four decimal places.
• Work Done: The calculator computes the absolute value of the line integral, formatted with a ‘J’ suffix to indicate joules, rounded to four decimal places.

Review all input data to ensure precision in the results, and utilize these calculations to further analyze vector fields or physical systems as necessary.