Question 14 (MCQ) - Chapter 8 Class 12 Application of Integrals (Important Question)

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Misc 19

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Misc 19 The area bounded by the π¦-axis, π¦=cosβ‘π₯ and π¦=sinβ‘π₯ when 0β€π₯β€π/2 is (A) 2 ( β("2 β1" )) (B) β("2 β1" ) (C) β("2 " )+1 (D) β("2 " )
Finding point of intersection B
Solving
π¦=cosβ‘π₯ and π¦=sππβ‘π₯
cosβ‘π₯=sππβ‘π₯
At π₯=π/4 , both are equal
Also,
π¦=cosβ‘π₯ = cos π/4 = 1/β2
So, B =((π )/4 , 1/β2)
Area Required
Area Required = Area ABCO β Area BCO
Area ABCO
Area ABCO = β«_0^(π/4)βγπ¦ ππ₯γ
Here, π¦=cosβ‘π₯
Thus,
Area ABCO =β«_0^(π/4)βγcosβ‘π₯ ππ₯γ
=[sinβ‘π₯ ]_0^(π/4)
=[sinβ‘γπ/4βsinβ‘0 γ ]
=1/β2β0
=1/β2
Area BCO
Area BCO = β«_0^(π/4)βγπ¦ ππ₯γ
Here, π¦=sinβ‘π₯
Thus,
Area BCO =β«_0^(π/4)βγsinβ‘π₯ ππ₯γ
=[γβcππ γβ‘π₯ ]_0^(π/4)
=β[cosβ‘γπ/4βcosβ‘(0) γ ]
=β[1/β2β1]
=1β1/β2
Therefore
Area Required = Area ABCO β Area BCO
=1/β2β[1β1/β2]
=1/β2+1/β2β1
=2/β2β1
=βπβπ
β΄ Option B is Correct

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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