This document provides calculus practice problems for students. It includes instructions to integrate specific functions like sec2x and x2/(x3 + 1) using integration guidelines. Students are also tasked with deriving the tangent formula of integration using logarithmic rules and trigonometric identities. One independent practice problem asks students to find the average value of the function f(x) = tan x between 0 and pi/4.

1. AP Calculus Warm up
2.8.18
Integrate:
𝜋
6
𝜋
𝑠𝑒𝑐2
𝑥 𝑑𝑥
𝑥2
𝑥3 + 1
𝑑𝑥

2. Guidelines for integration
page 337

7. Practice Problems
1. Derive the tangent formula of integration using the
log rule and trig identities.

8. Independent Practice
1. Find the average value of f(x) = tan x on [0, pi/4 ]
Recall: