CALCULUS II PRACTICE FINAL EXAM

CALCULUS II PRACTICE FINAL EXAM

BASIC INTEGRATION (1–15)

1. ∫ x dx
A. x² + C
B. x²/2 + C
C. 2x + C
D. ln x + C
Answer: B
Power rule: increase exponent and divide by new exponent.



2. ∫ 1/x dx
A. 1/x²
B. x
C. ln|x| + C
D. e^x
Answer: C
Standard logarithmic integral form.



3. ∫ e^x dx
A. x e^x
B. e^x + C
C. ln x
D. 1/e^x
Answer: B
Derivative of e^x is itself.



4. ∫ cos x dx
A. -cos x
B. sin x + C
C. -sin x + C
D. tan x
Answer: B
Integral of cosine is sine.



5. ∫ sin x dx
A. cos x
B. -cos x + C
C. sin x
D. tan x

,Answer: B
Derivative of cos is -sin.



6. ∫ x² dx
A. x³/3 + C
B. 2x + C
C. x²/2
D. ln x
Answer: A
Power rule application.



7. ∫ 2x dx
A. x² + C
B. 2x²
C. x
D. ln x
Answer: A
Constant multiple rule.



8. ∫ (x + 3) dx
A. x²/2 + 3x + C
B. x + 3
C. ln x + 3
D. x³
Answer: A
Integrate term-by-term.



9. ∫ sec²x dx
A. sec x
B. tan x + C
C. -tan x
D. cot x
Answer: B
Derivative of tan x is sec²x.



10. ∫ csc²x dx
A. cot x
B. -cot x + C
C. tan x
D. sec x
Answer: B
Derivative of cot is -csc².

, 11. ∫ sec x tan x dx
A. sec x + C
B. tan x
C. ln x
D. cos x
Answer: A
Derivative of sec x is sec x tan x.



12. ∫ 1/(1+x²) dx
A. tan⁻¹x + C
B. ln x
C. sin x
D. cos x
Answer: A
Inverse tangent formula.



13. ∫ 1/√(1-x²) dx
A. cos⁻¹x
B. sin⁻¹x + C
C. ln x
D. tan x
Answer: B
Inverse sine formula.



14. ∫ 5 dx
A. x⁵
B. 5x + C
C. ln x
D. 1/x
Answer: B
Constant integration rule.



15. ∫ x³ dx
A. x⁴/4 + C
B. 3x²
C. ln x
D. x²
Answer: A
Power rule.



TECHNIQUES OF INTEGRATION (16–35)