6. Integration and Accumulation of Change

Integrating Using Substitution — Quiz

Test your understanding of integrating using substitution with 5 practice questions.

Practice Questions

Question 1

In integration by substitution, what is the main goal of introducing a new variable such as $u$?

Question 2

What is the derivative of $u = x^2 + 1$ with respect to $x$?

Question 3

What is the value of $\int 2x\cos(x^2)\,dx$ using substitution?

Question 4

Which substitution is most useful for evaluating $\int \frac{1}{3x+5}\,dx$?

Question 5

After substituting $u = x^2 + 4$, what is the new integrand form of $\int x(x^2+4)^3\,dx$ in terms of $u$ and $du$?