2. Pure Calculus

Integration — Quiz

Test your understanding of integration with 5 practice questions.

Practice Questions

Question 1

Consider the integral $ \int \frac{1}{x^3 - x} \, dx $. Which of the following is the most appropriate first step for evaluating this integral?

Question 2

Evaluate the indefinite integral $ \int x e^{-x} \, dx $.

Question 3

To evaluate the definite integral $ \int_{0}^{\frac{\pi}{2}} \sin^3(x) \cos^2(x) \, dx $, which of the following substitutions would be most effective?

Question 4

When using the Trapezoidal Rule to approximate the definite integral $ \int_{a}^{b} f(x) \, dx $, what is the effect of increasing the number of subintervals, $n$?

Question 5

Evaluate the indefinite integral $ \int \frac{1}{x^2 + 2x + 2} \, dx $.