Indefinite Integral Quiz for High School Calculus

📚 Quick Study Guide

• 🔍 Definition: An indefinite integral is a function that takes the antiderivative of another function. It represents a family of functions differing by a constant.
• ➕ Constant of Integration: Always add '$+C$' to the end of an indefinite integral, representing the arbitrary constant.
• ➗ Power Rule: $\int x^n dx = \frac{x^{n+1}}{n+1} + C$, where $n \neq -1$.
• 💡 Special Case: $\int x^{-1} dx = \int \frac{1}{x} dx = \ln|x| + C$.
• 🧪 Sum/Difference Rule: $\int [f(x) \pm g(x)] dx = \int f(x) dx \pm \int g(x) dx$.
• 🔢 Constant Multiple Rule: $\int k \cdot f(x) dx = k \int f(x) dx$, where $k$ is a constant.
• 📝 Common Integrals: $\int \sin(x) dx = -\cos(x) + C$, $\int \cos(x) dx = \sin(x) + C$, $\int e^x dx = e^x + C$.

🤔 Practice Quiz

1. What is the indefinite integral of $x^2$?
   1. $\frac{x^3}{3} + C$
   2. $2x + C$
   3. $x^3 + C$
   4. $\frac{x^2}{2} + C$
2. What is the indefinite integral of $5x^4$?
   1. $x^5 + C$
   2. $20x^3 + C$
   3. $5x^5 + C$
   4. $\frac{5}{4}x^5 + C$
3. What is the indefinite integral of $\sin(x)$?
   1. $\cos(x) + C$
   2. $-\cos(x) + C$
   3. $\sin(x) + C$
   4. $-\sin(x) + C$
4. What is the indefinite integral of $e^x$?
   1. $e^x + C$
   2. $xe^{x-1} + C$
   3. $\frac{e^{x+1}}{x+1} + C$
   4. $e^{-x} + C$
5. What is the indefinite integral of $\frac{1}{x}$?
   1. $x + C$
   2. $\ln|x| + C$
   3. $x^{-2} + C$
   4. $-\frac{1}{x^2} + C$
6. What is the indefinite integral of $3x^2 + 2x$?
   1. $x^3 + x^2 + C$
   2. $6x + 2 + C$
   3. $x^3 + x^2 + x + C$
   4. $\frac{3x^3}{3} + \frac{2x^2}{2} + C$
7. What is the indefinite integral of $0$?
   1. $1 + C$
   2. $0 + C$
   3. $C$
   4. $x + C$