Indefinite Integrals Objective Questions

Indefinite Integrals Objective Questions – Class 12 Maths

Indefinite Integrals Objective Questions

Class: CBSE Class 12
Subject: Mathematics
Section: Integrals
Topic: Indefinite Integrals Objective Questions
Exam Focus: CBSE Board Examinations

Instructions: These Multiple Choice Questions (MCQs) are designed strictly as per the NCERT syllabus, making them ideal for CBSE Class 12 Board Examination preparation. Each question includes a detailed explanation for clear conceptual understanding.

Q1. ∫ x⁵ dx = ?

a) x⁶/6 + C
b) 5x⁴ + C
c) x⁶ + C
d) x⁵/5 + C

Answer: a) x⁶/6 + C

Using power rule ∫ xⁿ dx = xⁿ⁺¹/(n+1) + C.

Q2. ∫ (1 + x²) dx = ?

a) x + x³/3 + C
b) x² + x³ + C
c) x + x² + C
d) 1 + 2x + C

Answer: a) x + x³/3 + C

Integrate each term separately.

Q3. ∫ sin 2x dx = ?

a) −cos 2x/2 + C
b) cos 2x + C
c) sin 2x/2 + C
d) −cos x + C

Answer: a) −cos 2x/2 + C

Use substitution: ∫ sin ax dx = −cos ax/a + C.

Q4. ∫ cos 3x dx = ?

a) sin 3x/3 + C
b) sin 3x + C
c) cos x + C
d) tan 3x + C

Answer: a) sin 3x/3 + C

Q5. ∫ 1/(1+x) dx = ?

a) ln|1+x| + C
b) 1/(1+x) + C
c) x + C
d) eˣ + C

Answer: a) ln|1+x| + C

Q6. ∫ tan x dx = ?

a) log|sec x| + C
b) sec x + C
c) sin x + C
d) tan²x + C

Answer: a) log|sec x| + C

Q7. ∫ cot x dx = ?

a) log|sin x| + C
b) tan x + C
c) sec x + C
d) cos x + C

Answer: a) log|sin x| + C

Q8. ∫ sec x tan x dx = ?

a) sec x + C
b) tan x + C
c) sin x + C
d) cos x + C

Answer: a) sec x + C

Q9. ∫ cosec x cot x dx = ?

a) −cosec x + C
b) cosec x + C
c) cot x + C
d) tan x + C

Answer: a) −cosec x + C

Q10. ∫ e³ˣ dx = ?

a) e³ˣ/3 + C
b) 3e³ˣ + C
c) eˣ + C
d) ln x + C

Answer: a) e³ˣ/3 + C

Q11. ∫ dx/(x²+1) = ?

a) tan⁻¹x + C
b) sin⁻¹x + C
c) sec⁻¹x + C
d) log x + C

Answer: a) tan⁻¹x + C

Q12. ∫ dx/(√(1−x²)) = ?

a) sin⁻¹x + C
b) cos⁻¹x + C
c) tan⁻¹x + C
d) sec⁻¹x + C

Answer: a) sin⁻¹x + C

Q13. ∫ log x dx = ?

a) x log x − x + C
b) log x + C
c) x² + C
d) 1/x + C

Answer: a) x log x − x + C

Q14. ∫ √(1+x) dx = ?

a) 2/3 (1+x)³ᐟ² + C
b) √(1+x) + C
c) (1+x)² + C
d) log(1+x)

Answer: a) 2/3 (1+x)³ᐟ² + C

Q15. ∫ (2x+1) dx = ?

a) x² + x + C
b) 2x² + C
c) x² + C
d) 2x + 1

Answer: a) x² + x + C

Q16. ∫ dx = ?

a) x + C
b) 1
c) C
d) 0

Answer: a) x + C

Q17. ∫ (sec²x + cosec²x) dx = ?

a) tan x − cot x + C
b) tan x + cot x + C
c) sec x + cosec x
d) sin x + cos x

Answer: a) tan x − cot x + C

Q18. ∫ a dx = ? (a constant)

a) ax + C
b) a + C
c) x + C
d) a²x

Answer: a) ax + C

Q19. ∫ (eˣ + sin x) dx = ?

a) eˣ − cos x + C
b) eˣ + cos x + C
c) eˣ + sin x
d) sin x − eˣ

Answer: a) eˣ − cos x + C

Q20. If ∫ f(x) dx = F(x) + C, then F′(x) = ?

a) f(x)
b) C
c) 0
d) x

Answer: a) f(x)

By definition of indefinite integration and the Fundamental Theorem of Calculus.

Indefinite Integrals Objective Questions

Indefinite Integrals Objective Questions

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