MATH 221 Lecture Notes - Lecture 17: Antiderivative

Comparing Antiderivatives

(a) Explain why the antiderivative is equivalent to the antiderivative .

(b) Explain why the antiderivative , is equivalent to die antiderivative .

Use a computer algebra system to find the integral. Use the computer algebra system to graph two antiderivatives. Describe the relationship between the graph of the two antiderivative.

Comparing Integrals Consider the integral

(a) Find the integral by completing the square of the radicand.

(b) Find the integral by making the substitution .

(c) The antiderivatives in pans (a) and (b) appear to be significantly different. Use a graphing utility to graph each antiderivative in the same viewing window and determine the relationship between them. Find the domain of each.