Integration Using Substitution MCQs

Integration Using Substitution MCQs – Class 12 Maths

Integration Using Substitution MCQs

Class: CBSE Class 12
Subject: Mathematics
Section: Integrals
Topic: Integration Using Substitution MCQs
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 solution highlights substitution techniques for conceptual clarity.

Key Concept:

If ∫ f(g(x))·g′(x) dx = ∫ f(u) du where u = g(x)

Q1. ∫ 2x (x²+1)³ dx = ?

a) (x²+1)⁴/4 + C
b) (x²+1)³
c) x²+1
d) 2x

Answer: a) (x²+1)⁴/4 + C

Let u=x²+1 ⇒ du=2x dx.

Q2. ∫ cos(3x) dx = ?

a) sin3x/3 + C
b) sin3x
c) cosx
d) tanx

Answer: a) sin3x/3 + C

Q3. ∫ sin(5x) dx = ?

a) −cos5x/5 + C
b) cos5x
c) sinx
d) tanx

Answer: a) −cos5x/5 + C

Q4. ∫ e²ˣ dx = ?

a) e²ˣ/2 + C
b) eˣ
c) 2eˣ
d) ln x

Answer: a) e²ˣ/2 + C

Q5. ∫ 1/(x+1) dx = ?

a) ln|x+1| + C
b) 1/x
c) x
d) eˣ

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

Q6. ∫ x/(x²+1) dx = ?

a) 1/2 ln(x²+1) + C
b) ln x
c) tan⁻¹x
d) x²

Answer: a) 1/2 ln(x²+1) + C

Q7. ∫ 2x/(x²+5) dx = ?

a) ln(x²+5) + C
b) x²
c) tan⁻¹x
d) 1/x

Answer: a) ln(x²+5) + C

Q8. ∫ sec²(3x) dx = ?

a) tan3x/3 + C
b) tanx
c) secx
d) cotx

Answer: a) tan3x/3 + C

Q9. ∫ cosec²(4x) dx = ?

a) −cot4x/4 + C
b) cotx
c) tanx
d) secx

Answer: a) −cot4x/4 + C

Q10. ∫ 1/√(x+2) dx = ?

a) 2√(x+2) + C
b) √x
c) ln x
d) x²

Answer: a) 2√(x+2) + C

Q11. Best substitution for ∫ x√(x²+1) dx ?

a) x²+1
b) √x
c) ln x
d) eˣ

Answer: a) x²+1

Q12. ∫ (2x+3)⁵ dx uses?

a) Substitution
b) Parts
c) Limits
d) Identity

Answer: a) Substitution

Q13. ∫ 1/(a+bx) dx = ?

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

Answer: a) 1/b ln|a+bx| + C

Q14. ∫ √(3x+1) dx = ?

a) 2(3x+1)³ᐟ²/9 + C
b) √x
c) x²
d) ln x

Answer: a) 2(3x+1)³ᐟ²/9 + C

Q15. ∫ (x+1)⁻¹ dx = ?

a) ln|x+1| + C
b) x
c) 1/x
d) eˣ

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

Q16. ∫ e^(x+2) dx = ?

a) e^(x+2) + C
b) eˣ
c) x²
d) ln x

Answer: a) e^(x+2) + C

Q17. ∫ sin²(3x) dx requires?

a) Identity + Substitution
b) Parts
c) Direct
d) Limits

Answer: a) Identity + Substitution

Q18. ∫ 3x² e^(x³) dx = ?

a) e^(x³) + C
b) x³
c) ln x
d) eˣ

Answer: a) e^(x³) + C

Q19. ∫ 1/(√(1−x²)) dx = ?

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

Answer: a) sin⁻¹x + C

Q20. Substitution method simplifies integrals by?

a) Changing variable
b) Differentiation
c) Limits
d) Graph

Answer: a) Changing variable

Integration Using Substitution MCQs

Integration Using Substitution MCQs

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