Ex 7.8, 22 (MCQ) - Chapter 7 Class 12 Integrals (Important Question)
Last updated at August 18, 2026 by Teachoo
Chapter 7 Class 12 Integrals
Ex 7.1, 10
Important
You are here
You are here
Maths Class 12
Important Questions for exams Class 12
- Chapter 1 Class 12 Relation and Functions
- Chapter 2 Class 12 Inverse Trigonometric Functions
- Chapter 3 Class 12 Matrices
- Chapter 4 Class 12 Determinants
- Chapter 5 Class 12 Continuity and Differentiability
- Chapter 6 Class 12 Application of Derivatives
-
Chapter 7 Class 12 Integrals
- Chapter 8 Class 12 Application of Integrals
- Chapter 9 Class 12 Differential Equations
- Chapter 10 Class 12 Vector Algebra
- Chapter 11 Class 12 Three Dimensional Geometry
- Chapter 12 Class 12 Linear Programming
- Chapter 13 Class 12 Probability
Transcript
Ex 7.8, 22 Choose the correct answer ∫_0^(2/3)▒𝑑𝑥/(4 +9𝑥^2 ) equals (A) 𝜋/6 (B) 𝜋/12 (C) 𝜋/24 (D) 𝜋/4 Step 1 :- Let F(𝑥)=∫1▒𝑑𝑥/(4 + 9𝑥^2 ) Divide and multiply the integrate by 4 =∫1▒█(𝑑𝑥@4)/((4 + 9𝑥^2)/4) =1/4 ∫1▒𝑑𝑥/(1 + 9/4 𝑥^2 ) =1/4 ∫1▒𝑑𝑥/(1 + (3/2 𝑥)^2 ) Put 3/2 𝑥=𝑡 Differentiating w.r.t.𝑥 𝑑(3/2 𝑥)/𝑑𝑥=𝑑𝑡/𝑑𝑥 3/2=𝑑𝑡/𝑑𝑥 𝑑𝑥=𝑑𝑡/(3/2) 𝑑𝑥=2/3 𝑑𝑡 Hence 1/4 ∫1▒〖𝑑𝑥/(1+(3/2 𝑥)^2 )=1/4 ∫1▒〖1/(1+𝑡^2 ) 2/3〗 𝑑𝑡〗 =1/4 × 2/3 ∫1▒𝑑𝑡/(1+𝑡^2 ) =1/6 tan^(−1)𝑡 Putting 𝑡=3/2 𝑥 =1/6 tan^(−1)〖3/2 𝑥〗 Hence F(𝑥)=1/6 tan^(−1)〖3/2 𝑥〗 Step 2 :- ∫_0^(2/3)▒〖𝑑𝑥/(4+9𝑥^2 )=𝐹(2/3)−𝐹(0) 〗 =1/6 tan^(−1)〖(3/2 × 2/3)−1/6 tan^(−1)(0) 〗 =1/6 tan^(−1)〖(1)−1/6 tan^(−1)(0) 〗 =1/6 × 𝜋/4−0 =𝜋/24 ∵ Option (C) is correct.
