CALCULUS II EXAMINATION QUESTIONS AND CORRECT ANSWER WITH EXPLANATION GRADED A+ STUDYGUIDE

CALCULUS II EXAMINATION QUESTIONS AND CORRECT
ANSWER WITH EXPLANATION GRADED A+ STUDYGUIDE
SOUTHERN NEW HAMPSHIRE UNIVERSITY
1. Calculus II mainly focuses on:
A. Integration techniques and applications
B. Basic arithmetic
C. Geometry only
D. Biology
Answer: A
Rationale: Calc II extends integration and series.

2. Integration is the reverse of:
A. Differentiation
B. Addition
C. Multiplication
D. Graphing
Answer: A
Rationale: Integration undoes derivatives.

3. The integral of xⁿ dx (n ≠ -1) is:
A. xⁿ⁺¹/(n+1) + C
B. nxⁿ⁻¹
C. xⁿ
D. ln x
Answer: A
Rationale: Power rule for integration.

4. ∫ 1/x dx equals:
A. ln|x| + C
B. x²
C. 1/x²
D. e^x
Answer: A
Rationale: Logarithmic integral.

5. Substitution method is used to:
A. Simplify integrals

, B. Solve derivatives
C. Find limits only
D. Graph functions
Answer: A
Rationale: Reverse chain rule.

6. Integration by parts formula is:
A. ∫u dv = uv − ∫v du
B. u + v
C. u/v
D. uv
Answer: A
Rationale: Product integration rule.

7. Integration by parts is based on:
A. Product rule
B. Chain rule
C. Quotient rule
D. Power rule
Answer: A
Rationale: Derived from differentiation.

8. A definite integral gives:
A. Area under curve
B. Slope
C. Limit only
D. Function value
Answer: A
Rationale: Accumulated area.

9. Limits at infinity describe:
A. End behavior
B. Local slope
C. Derivative
D. Constant
Answer: A
Rationale: Behavior as x → ∞.

10. Improper integrals involve:
A. Infinite limits or discontinuities

, B. Simple polynomials
C. Algebra only
D. Constants
Answer: A
Rationale: Non-standard integrals.

11. A convergent integral:
A. Has a finite value
B. Is infinite
C. Does not exist
D. Is undefined
Answer: A
Rationale: Finite result.

12. A divergent integral:
A. Does not converge
B. Has finite value
C. Always zero
D. Is constant
Answer: A
Rationale: Infinite or undefined.

13. The average value of a function is found using:
A. Definite integral
B. Derivative
C. Limit
D. Algebra
Answer: A
Rationale: Integral-based average.

14. A sequence is:
A. Ordered list of numbers
B. Graph
C. Function only
D. Equation
Answer: A
Rationale: Number progression.

15. A series is:
A. Sum of sequence terms