# Misc 19 - Chapter 8 Class 12 Application of Integrals (Important Question)

Last updated at May 29, 2018 by Teachoo

Last updated at May 29, 2018 by Teachoo

Transcript

Misc 19 The area bounded by the 𝑦-axis, 𝑦=cos𝑥 and 𝑦=sin𝑥 when 0≤𝑥≤ 𝜋2 is (A) 2 ( 2 −1) (B) 2 −1 (C) 2 +1 (D) 2 Finding point of intersection B Solving 𝑦=cos𝑥 and 𝑦=s𝑖𝑛𝑥 cos𝑥=s𝑖𝑛𝑥 At 𝑥= 𝜋4 , both are equal Also, 𝑦=cos𝑥 = cos 𝜋4 = 1 2 So, B = 𝜋 4 , 1 2 Step 3: Finding Area Area Required = Area ABCO – Area BCO Area ABCO Area ABCO = 0 𝜋4𝑦 𝑑𝑥 Here, 𝑦= cos𝑥 Thus, Area ABCO = 0 𝜋4 cos𝑥 𝑑𝑥 = sin𝑥0 𝜋4 = sin 𝜋4− sin0 = 1 2−0 = 1 2 Area BCO Area BCO = 0 𝜋4𝑦 𝑑𝑥 Here, 𝑦= sin𝑥 Thus, Area BCO = 0 𝜋4 sin𝑥 𝑑𝑥 = −c𝑜𝑠𝑥0 𝜋4 =− cos 𝜋4− cos 0 =− 1 2−1 =1− 1 2 Therefore Area Required = Area ABCO – Area BCO = 1 2− 1− 1 2 = 1 2+ 1 2−1 = 2 2−1 = 2−1 ∴ Option B is Correct

Chapter 8 Class 12 Application of Integrals

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

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.