Indefinite integration homework

1 7.1 Indefinite Integrals Calculus Learning Objectives A student will be able to:  Find antiderivatives of functions.  Represent antiderivatives.  Interpret the constant of integration graphically.  Solve differential equations.  Use basic antidifferentiation techniques.  Use basic integration rules. Introduction

We have a particular sign and set of symbols we use to indicate integration: 2 We refer to the left side of the equation as “the indefinite integral of with respect to " The function is called the integrandand the constant is called the constant of integration.

As with differentiation, we can develop several rules for dealing with a finite number of integrable functions. They are stated as follows: 3 If and are integrable functions, and is a constant, then Example 2: Compute the following indefinite integral.

The term indefinite integral is a synonym for antiderivative. Note: Differentiation and anti-differentiation are “inverse” operations of each other. That is, if you find the antiderivative of a function f, then take the derivative, you will end up back at f. Similarly, if you take the derivative, the antiderivative takes you back.