Q1: 1. In calculus, the integral of a function represents

• A) The area under the curve
• B) The slope of the curve
• C) The maximum value of the function
• D) The average rate of change of the function

Q2: 2. What is the integral of the function f(x) = 3x^2?

• A) x^2
• B) 3x^3 + C
• C) 3x + C
• D) 3x^3

Q3: 3. The process of finding the integral of a function is also known as

• A) Differentiation
• B) Integration
• C) Derivation
• D) Summation

Q4: 4. Which of the following is used to represent the indefinite integral of a function?

• A) ∫f(x) dx
• B) f'(x)
• C) ∫∫f(x) dx
• D) d/dx(f(x))

Q5: 5. What is the integral of the function f(x) = sin(x)?

• A) cos(x) + C
• B) sin(x) + C
• C) -cos(x) + C
• D) -sin(x) + C

Q6: 6. The definite integral of a function represents

• A) The area under the curve
• B) The slope of the curve
• C) The maximum value of the function
• D) The average rate of change of the function over a specific interval

Q7: 7. What is the integral of the function f(x) = 1/x?

• A) ln(x) + C
• B) x + C
• C) 1/x + C
• D) e^x + C

Q8: 8. The fundamental theorem of calculus relates integration to

• A) Derivatives
• B) Limits
• C) Matrices
• D) Trigonometry

Q9: 9. Which of the following properties of integrals is true?

• A) ∫(f(x) + g(x)) dx = ∫f(x) dx + ∫g(x) dx
• B) ∫(f(x) * g(x)) dx = ∫f(x) dx * ∫g(x) dx
• C) ∫(f(x) - g(x)) dx = ∫f(x) dx - ∫g(x) dx
• D) ∫(f(x)/g(x)) dx = ∫f(x) dx / ∫g(x) dx

Q10: 10. What is the integral of the function f(x) = e^x?

• A) e^x + C
• B) ln(x) + C
• C) x + C
• D) cos(x) + C

Q11: 11. The symbol used to represent integration is

• A) ∆x
• B) Σ
• C) ∫
• D) ∇

Q12: 12. What is the integral of the function f(x) = 2x + 3?

• A) x^2 + 3x + C
• B) x^2 + 3 + C
• C) x^2 + C
• D) 2x^2 + 3x + C

Q13: 13. The process of finding the area under a curve using integrals is known as

• A) Riemann sum
• B) Trapezoidal rule
• C) Simpson's rule
• D) Integrating

Q14: 14. Which of the following is NOT a method of integration?

• A) Substitution
• B) Differentiation
• C) Integration by parts
• D) Partial fractions

Q15: 15. What is the integral of the function f(x) = 1/x^2?

• A) -1/x + C
• B) ln(x) + C
• C) -1/x^3 + C
• D) 1/x + C

Q16: 16. The definite integral of a function over an interval can be interpreted as

• A) The average value of the function over that interval
• B) The maximum value of the function
• C) The slope of the curve at a specific point
• D) The area under the curve within that interval

Q17: 17. What is the integral of the function f(x) = cos(x)?

• A) sin(x) + C
• B) -cos(x) + C
• C) cos(x) + C
• D) -sin(x) + C

Q18: 18. The definite integral of a function represents the

• A) Area under the curve between two specific points
• B) Slope of the curve at a single point
• C) Maximum value of the function
• D) Average rate of change of the function

Q19: 19. What is the integral of the function f(x) = 4x^3?

• A) 4x + C
• B) x^4 + C
• C) x^3 + C
• D) x^4 + C

Q20: 20. Which of the following is NOT true about the definite integral of a function?

• A) It can be negative
• B) It represents the area under the curve
• C) It is always positive
• D) It can be zero

Q21: 21. What is the integral of the function f(x) = e^(2x)?

• A) (1/2)e^(2x) + C
• B) e^(2x) + C
• C) 2e^(2x) + C
• D) (1/2)e^(2x^2) + C

Q22: 22. The integral of a constant function is

• A) The constant itself
• B) The constant multiplied by x
• C) Zero
• D) The constant divided by x

Q23: 23. What is the integral of the function f(x) = 1/(1+x^2)?

• A) tan^(-1)(x) + C
• B) ln(1+x^2) + C
• C) sin^(-1)(x) + C
• D) e^(1+x^2) + C

Q24: 24. The integral of a function gives us the

• A) Maximum value of the function
• B) Average value of the function
• C) Minimum value of the function
• D) Derivative of the function

Q25: 25. What is the integral of the function f(x) = x^2 + 2x + 1?

• A) (1/3)x^3 + x^2 + x + C
• B) x^3 + 2x^2 + x + C
• C) (1/3)x^3 + x^2 + 1 + C
• D) x^3 + 2x + 1 + C