12. Applications of Residues

Improper Real Integrals — Quiz

Test your understanding of improper real integrals with 5 practice questions.

Practice Questions

Question 1

Which feature makes the integral $\int_0^\infty e^{-x}\,dx$ an improper real integral?

Question 2

When using residues to evaluate $\int_{-\infty}^{\infty} f(x)\,dx$, which contour is commonly used if the poles are in the upper half-plane and the arc contribution vanishes?

Question 3

Which theorem gives $\oint_C f(z)\,dz = 2\pi i$ times the sum of residues inside $C$?

Question 4

What is $\int_{-\infty}^{\infty} \frac{dx}{x^2+1}$?

Question 5

What is the Cauchy principal value of $\int_{-1}^{1} \frac{dx}{x}$?