Integrals MCQs Class 12 Maths (NCERT Based)

Class: CBSE Class 12
Subject: Mathematics
Section: Integrals
Topic: Integrals MCQs with Answers & Explanations
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 concept clarity.

Q1. ∫ x² dx is equal to:

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

Answer: a) x³/3 + C

Explanation: Using power rule: ∫ xⁿ dx = xⁿ⁺¹/(n+1) + C. Here n = 2.

Q2. ∫ cos x dx equals:

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

Answer: a) sin x + C

Explanation: Derivative of sin x is cos x, hence its integral is sin x + C.

Q3. ∫ eˣ dx equals:

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

Answer: a) eˣ + C

Explanation: The function eˣ is its own derivative and integral.

Q4. ∫ 1/x dx equals:

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

Answer: a) log x + C

Explanation: Standard integral: ∫ 1/x dx = ln|x| + C.

Q5. ∫ sin x dx equals:

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

Answer: b) −cos x + C

Explanation: Since derivative of cos x is −sin x, integral of sin x is −cos x.

Q6. ∫ sec²x dx = ?

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

Answer: a) tan x + C

Derivative of tan x is sec²x.

Q7. ∫ cosec²x dx = ?

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

Answer: b) −cot x + C

Derivative of cot x is −cosec²x.

Q8. ∫ dx/(1+x²) = ?

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

Answer: a) tan⁻¹x + C

Q9. ∫ dx/√(1−x²) = ?

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

Answer: a) sin⁻¹x + C

Q10. ∫ 2x dx = ?

a) x² + C
b) 2x² + C
c) x²/2 + C
d) 2 + C

Answer: a) x² + C

Q11. ∫ (3x² + 2) dx = ?

a) x³ + 2x + C
b) x³ + C
c) 3x³ + 2x + C
d) x³ + x + C

Answer: a) x³ + 2x + C

Q12. ∫ e²ˣ dx = ?

a) e²ˣ/2 + C
b) 2e²ˣ + C
c) eˣ + C
d) ln x + C

Answer: a) e²ˣ/2 + C

Q13. ∫ aˣ dx = ?

a) aˣ/ln a + C
b) ln aˣ + C
c) aˣ + C
d) xᵃ + C

Answer: a) aˣ/ln a + C

Q14. ∫ 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

Q15. ∫ √x dx = ?

a) 2/3 x³ᐟ² + C
b) x³ᐟ² + C
c) √x + C
d) x² + C

Answer: a) 2/3 x³ᐟ² + C

Q16. ∫ 1/√x dx = ?

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

Answer: a) 2√x + C

Q17. ∫ (sin x + cos x) dx = ?

a) −cos x + sin x + C
b) sin x + cos x + C
c) tan x + C
d) 0

Answer: a) −cos x + sin x + C

Q18. ∫ 0 dx = ?

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

Answer: a) C

Q19. ∫ k dx (k constant) = ?

a) kx + C
b) k + C
c) x + C
d) k²x

Answer: a) kx + C

Q20. If ∫ f(x) dx = F(x), then derivative of F(x) is:

a) f(x)
b) 0
c) 1
d) x

Answer: a) f(x)

This is the Fundamental Theorem of Calculus.

Integrals MCQs Class 12 Maths (NCERT Based)

Integrals MCQs Class 12 Maths (NCERT Based)

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