Illustrative Examples for Antiderivatives of Trigonometric Functions

📚 Quick Study Guide

• 📐 The antiderivative of $\sin(x)$ is $-\cos(x) + C$. Remember the negative sign!
• 🧭 The antiderivative of $\cos(x)$ is $\sin(x) + C$. No negative sign here.
• 📈 The antiderivative of $\sec^2(x)$ is $\tan(x) + C$. This is a common one.
• 🔗 The antiderivative of $\csc^2(x)$ is $-\cot(x) + C$. Watch out for the negative.
• 💡 The antiderivative of $\sec(x)\tan(x)$ is $\sec(x) + C$.
• 🧪 The antiderivative of $\csc(x)\cot(x)$ is $-\csc(x) + C$. Negative again!
• 📝 Remember the constant of integration, $C$, for all indefinite integrals.
• ➕ Don't forget u-substitution can be your best friend for more complex problems.

Practice Quiz

1. What is the antiderivative of $\sin(x)$?
   1. $\cos(x) + C$
   2. $-\cos(x) + C$
   3. $\sec(x) + C$
   4. $-\sec(x) + C$
2. What is the antiderivative of $\cos(x)$?
   1. $\sin(x) + C$
   2. $-\sin(x) + C$
   3. $\tan(x) + C$
   4. $-\tan(x) + C$
3. What is the antiderivative of $\sec^2(x)$?
   1. $\tan(x) + C$
   2. $\cot(x) + C$
   3. $\sec(x) + C$
   4. $\csc(x) + C$
4. What is the antiderivative of $\csc^2(x)$?
   1. $\tan(x) + C$
   2. $-\cot(x) + C$
   3. $\sec(x) + C$
   4. $-\csc(x) + C$
5. What is the antiderivative of $\sec(x)\tan(x)$?
   1. $\sec(x) + C$
   2. $\tan(x) + C$
   3. $\csc(x) + C$
   4. $\cot(x) + C$
6. What is the antiderivative of $\csc(x)\cot(x)$?
   1. $\sec(x) + C$
   2. $-\csc(x) + C$
   3. $\csc(x) + C$
   4. $-\cot(x) + C$
7. What is the antiderivative of $2\sin(x)$?
   1. $2\cos(x) + C$
   2. $-2\cos(x) + C$
   3. $\cos(2x) + C$
   4. $-\cos(2x) + C$