Derivatives & Integrals

Objectives: When you complete this module, you will be able to:

Text References: none

Homework Problems: none

Introduction:

 The derivatives you'll need to know are:

The last case essentially states that the derivative is distributive.  You'll also need the product and quotient rules.  I am assuming that u and v are functions of time, since most of your problems will involve functions which depend on time.

 Here are the derivatives of the sine and cosine:

The integral is just going in reverse:

The first is called the indefinite integral.  You should verify that it works by taking the derivative of the right side.  Since the derivative of the constant C is zero, you can see that any constant will satisfy the integral.  The second is called the definite integral.  "a" and "b" are called the "limits."  You follow the same procedure to find the integral (as with the indefinite) but then you apply the limits - "upper limits minus lower limits" - the definite integral yields a value if the limits are numeric.

Example 1: Derivative - Power Law and Polynomials

Example 2: Derivative - Power Law and Trigonometric Functions

Example 3: Indefinite Integrals - Power Law and Polynomials

Example 4: Definite Integrals - Power Law and Polynomials