# Misc 19

Last updated at March 11, 2017 by Teachoo

Last updated at March 11, 2017 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

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.