Definite Integrals MCQs with Solutions
Definite Integrals MCQs with Solutions
Class: CBSE Class 12
Subject: Mathematics
Section: Integrals
Topic: Definite Integrals MCQs with Solutions
Exam Focus: CBSE Board Examinations
Subject: Mathematics
Section: Integrals
Topic: Definite Integrals MCQs with Solutions
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. Detailed explanations are provided for concept clarity.
Q1. ∫₀¹ x dx = ?
Answer: a) 1/2
∫ x dx = x²/2. Applying limits 0 to 1 ⇒ 1/2.
∫ x dx = x²/2. Applying limits 0 to 1 ⇒ 1/2.
Q2. ∫₀¹ x² dx = ?
Answer: a) 1/3
Integral = x³/3 from 0 to 1.
Integral = x³/3 from 0 to 1.
Q3. ∫₀^π sin x dx = ?
Answer: a) 2
∫ sin x dx = −cos x. Evaluate between 0 and π.
∫ sin x dx = −cos x. Evaluate between 0 and π.
Q4. ∫₀^π cos x dx = ?
Answer: a) 0
sin π − sin 0 = 0.
sin π − sin 0 = 0.
Q5. ∫₀¹ eˣ dx = ?
Answer: a) e − 1
Q6. ∫₋₁¹ x³ dx = ?
Answer: a) 0
Odd function over symmetric limits ⇒ 0.
Odd function over symmetric limits ⇒ 0.
Q7. ∫₋₁¹ x² dx = ?
Answer: a) 2/3
Even function ⇒ 2∫₀¹ x² dx.
Even function ⇒ 2∫₀¹ x² dx.
Q8. ∫₀^a k dx = ?
Answer: a) ka
Q9. ∫₀^π sin²x dx = ?
Answer: a) π/2
Use identity sin²x = (1−cos2x)/2.
Use identity sin²x = (1−cos2x)/2.
Q10. ∫₀^π cos²x dx = ?
Answer: a) π/2
Q11. ∫₀¹ 1/(1+x²) dx = ?
Answer: a) π/4
Q12. ∫₀¹ (x+1) dx = ?
Answer: a) 3/2
Q13. ∫₁^e 1/x dx = ?
Answer: a) 1
ln e − ln 1 = 1.
ln e − ln 1 = 1.
Q14. ∫₀^{π/2} sin x dx = ?
Answer: a) 1
Q15. ∫₀^{π/2} cos x dx = ?
Answer: a) 1
Q16. ∫₀^a x dx = ?
Answer: a) a²/2
Q17. ∫₀^1 x³ dx = ?
Answer: a) 1/4
Q18. ∫₀^{π} (sin x + cos x) dx = ?
Answer: a) 2
Q19. ∫₀^{π/2} tan x dx = ?
Answer: a) ln 2
Q20. Fundamental Theorem: ∫ₐᵇ f′(x) dx = ?
Answer: a) f(b) − f(a)
Direct result of Fundamental Theorem of Calculus.
Direct result of Fundamental Theorem of Calculus.