Sure, here are 10 multiple-choice questions related to integration:
1. **What is the integral of \int 3x^2 \, dx ?**
- A) x^3 + C
- B) x^3 + 3x + C
- C) x^3 + 3x^2 + C
- D) x^3 + C
2. **Evaluate \int e^x \, dx .**
- A) e^x + C
- B) e^x
- C) \frac{e^x}{x} + C
- D) e^{x+1} + C
3. **Find the integral \int \frac{1}{x} \, dx .**
- A) \ln|x| + C
- B) \ln(x) + C
- C) \frac{1}{x} + C
- D) x + C
4. **What is the integral of \int \sin(x) \, dx ?**
- A) -\cos(x) + C
- B) \cos(x) + C
- C) -\sin(x) + C
- D) \sin(x) + C
5. **Evaluate \int x e^x \, dx using integration by parts.**
- A) x e^x - e^x + C
- B) x e^x + e^x + C
- C) e^x (x - 1) + C
- D) e^x (x + 1) + C
6. **What is the integral \int \cos^2(x) \, dx ?**
- A) \frac{x}{2} + \frac{\sin(2x)}{4} + C
- B) \frac{x}{2} - \frac{\sin(2x)}{4} + C
- C) \frac{x}{2} + \sin(x) \cos(x) + C
- D) \frac{x}{2} - \sin(x) \cos(x) + C
7. **Find the integral \int \frac{1}{1+x^2} \, dx .**
- A) \tan^{-1}(x) + C
- B) \ln|1+x^2| + C
- C) \frac{1}{x} + C
- D) \arctan(x) + C
8. **Evaluate \int \frac{2x}{1+x^2} \, dx .**
- A) \ln|1+x^2| + C
- B) \ln|x| + C
- C) \arctan(x) + C
- D) \frac{1}{2} \ln|1+x^2| + C
9. **What is the integral \int \sec^2(x) \, dx ?**
- A) \sec(x) + C
- B) \ln|\sec(x) + \tan(x)| + C
- C) \tan(x) + C
- D) \sec(x) + \tan(x) + C
10. **Find \int x^2 \ln(x) \, dx using integration by parts.**
- A) \frac{x^3 \ln(x)}{3} - \frac{x^3}{9} + C
- B) \frac{x^3 \ln(x)}{3} - \frac{x^3}{6} + C
- C) \frac{x^3 \ln(x)}{3} - \frac{x^3 \ln(2)}{6} + C
- D) \frac{x^3 \ln(x)}{3} - \frac{x^3}{6} + \frac{x^3}{9} + C
Feel free to use or modify these questions as needed!
