2. Further Pure 2

Advanced Calculus — Quiz

Test your understanding of advanced calculus with 5 practice questions.

Practice Questions

Question 1

When evaluating the improper integral $ \int_a^{\infty} f(x) dx $, which of the following is the correct limit definition?

Question 2

Which of the following integration techniques is most appropriate for evaluating integrals of the form $ \int P(x) e^{ax} dx $, where $ P(x) $ is a polynomial and $ a $ is a constant?

Question 3

Consider the integral $ I_n = \int x^n \cos(x) dx $. Which of the following is a valid reduction formula for $ I_n $?

Question 4

To find the volume of a solid generated by revolving the region bounded by $ y = f(x) $ and $ y = g(x) $ (where $ f(x) \ge g(x) $) from $ x = a $ to $ x = b $ around the y-axis, which integration method is most appropriate and what is the general formula?

Question 5

What is the result of integrating $ \int x^3 \ln(x) dx $ using integration by parts?