6. Integration and Accumulation of Change

Integrating Functions Using Long Division And Completing The Square — Quiz

Test your understanding of integrating functions using long division and completing the square with 5 practice questions.

Practice Questions

Question 1

Why is long division useful before integrating a rational function such as $\frac{x^2+1}{x-1}$?

Question 2

What is the first step in integrating $\int \frac{x^2+3x+2}{x+1}\,dx$ using long division?

Question 3

Complete the square for $x^2+6x+13$.

Question 4

Which antiderivative method is most directly suggested by an integrand of the form $\frac{1}{x^2+4x+8}$ after completing the square?

Question 5

Evaluate $\int (x^2+2x+1)\,dx$.