How to Integrate Y With Respect to X

Integration is one of the two corner stones of calculus. It is a process of summation that allows you to build complex solutions from simple building blocks. Integration of a function can be visualized by graphing the function and calculating the area between X-axis and the line on the graph. The process of integration divides the area under the graph into small building blocks and reconstructs the area from these blocks. To determine the area under the curve using integration, you add all the blocks that fill that area.

Instructions

    • 1

      Write the mathematical expression that represents the integration process. Use the symbol of an elongated S to represent the process of integration. Write the term YdX to the right of the elongated S so the expression appears as SYdX. A mathematical expression in this form is read as the integral of Y with respect to X.

    • 2

      Move Y to the left of the elongated S. Y is always treated as a constant if it is not given as a function of the variable X. By moving Y to the left of the integral sign, you are indicating that Y is not dependent on X and will therefore not be included in the integration process. Rather, Y will be multiplied by the result of the integration process. The mathematical expression becomes Y x (SdX). The expression is read as Y multiplied by the integral of dX.

    • 3

      Integrate dX. The result of integrating dX is X. Replace SdX with X.

    • 4

      Multiply X by the constant Y. The mathematical expression becomes Y x (X).

    • 5

      Add the integration constant C to the expression. The constant C represents an arbitrary constant value associated with an indefinite integral. The symbol C must be included for mathematical correctness. The result of integrating Y with respect to X is YX + C.

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