Integration by Parts MCQs Practice

Integration by Parts MCQs Practice – Class 12 Maths

Integration by Parts MCQs Practice

Class: CBSE Class 12
Subject: Mathematics
Section: Integrals
Topic: Integration by Parts MCQs Practice
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 uses the Integration by Parts formula for concept clarity.

Key Formula:

∫ u·v dx = u∫v dx − ∫(du/dx · ∫v dx) dx

Q1. ∫ x eˣ dx = ?

a) (x−1)eˣ + C
b) (x+1)eˣ + C
c) xeˣ + C
d) eˣ + C

Answer: a) (x−1)eˣ + C

Take u=x, dv=eˣdx ⇒ Apply formula.

Q2. ∫ x sin x dx = ?

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

Answer: b) −x cos x + sin x + C

Q3. ∫ x cos x dx = ?

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

Answer: b) x sin x − cos x + C

Q4. ∫ x ln x dx = ?

a) x²/2 ln x − x²/4 + C
b) ln x + C
c) x ln x + C
d) x² ln x + C

Answer: a) x²/2 ln x − x²/4 + C

Q5. ∫ ln x dx = ?

a) x ln x − x + C
b) ln x + C
c) x + C
d) 1/x + C

Answer: a) x ln x − x + C

Q6. ∫ x² eˣ dx = ?

a) eˣ(x²−2x+2)+C
b) xeˣ + C
c) eˣ + C
d) x²eˣ

Answer: a) eˣ(x²−2x+2)+C

Q7. ∫ x² sin x dx = ?

a) −x²cosx+2xsinx+2cosx+C
b) x²sinx
c) sinx
d) cosx

Answer: a) −x²cosx+2xsinx+2cosx+C

Q8. ∫ x e²ˣ dx = ?

a) e²ˣ(2x−1)/4 + C
b) xe²ˣ
c) e²ˣ
d) ln x

Answer: a) e²ˣ(2x−1)/4 + C

Q9. ∫ x cos 2x dx = ?

a) x sin2x/2 + cos2x/4 + C
b) sin2x
c) cos2x
d) xcos2x

Answer: a) x sin2x/2 + cos2x/4 + C

Q10. ∫ x tan x dx = ?

a) x ln|secx| − ∫ ln|secx| dx
b) tanx
c) secx
d) x²

Answer: a) x ln|secx| − ∫ ln|secx| dx

Q11. First function in LIATE rule priority?

a) Logarithmic
b) Algebraic
c) Trigonometric
d) Exponential

Answer: a) Logarithmic

Q12. ∫ x·1 dx solved by parts gives?

a) x²/2 + C
b) x + C
c) 1
d) 0

Answer: a) x²/2 + C

Q13. ∫ eˣ sin x dx = ?

a) eˣ(sin x − cos x)/2 + C
b) eˣsinx
c) sinx
d) cosx

Answer: a) eˣ(sin x − cos x)/2 + C

Q14. ∫ eˣ cos x dx = ?

a) eˣ(sin x + cos x)/2 + C
b) eˣcosx
c) cosx
d) sinx

Answer: a) eˣ(sin x + cos x)/2 + C

Q15. ∫ x³ eˣ dx requires?

a) Repeated parts
b) Substitution
c) Partial fractions
d) Direct formula

Answer: a) Repeated parts

Q16. ∫ x ln²x dx uses?

a) Integration by parts
b) Substitution
c) Limits
d) None

Answer: a) Integration by parts

Q17. ∫ x·eˣ dx pattern result form?

a) Polynomial × eˣ
b) Log form
c) Trig form
d) Constant

Answer: a) Polynomial × eˣ

Q18. Best choice of u in ∫ x ln x dx?

a) ln x
b) x
c) 1
d) eˣ

Answer: a) ln x

Q19. ∫ x sin²x dx requires?

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

Answer: a) Identity + Parts

Q20. Integration by parts is derived from?

a) Product rule
b) Chain rule
c) Quotient rule
d) Limit definition

Answer: a) Product rule

It comes from differentiation of u·v.

Integration by Parts MCQs Practice

Integration by Parts MCQs Practice

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