Misc 17 (MCQ) - Chapter 8 Class 12 Application of Integrals (Term 2)
Last updated at Aug. 11, 2021 by Teachoo
Last updated at Aug. 11, 2021 by Teachoo
Transcript
Misc 17 The area bounded by the curve ๐ฆ = ๐ฅ |๐ฅ| , ๐ฅโ๐๐ฅ๐๐ and the ordinates ๐ฅ = โ 1 and ๐ฅ=1 is given by (A) 0 (B) 1/3 (C) 2/3 (D) 4/3 [Hint : ๐ฆ=๐ฅ2 if ๐ฅ > 0 ๐๐๐ ๐ฆ =โ๐ฅ2 if ๐ฅ < 0] We know that |๐ฅ|={โ(๐ฅ, ๐ฅโฅ0@&โ๐ฅ, ๐ฅ<0)โค Therefore, y = x|๐ฅ|={โ(๐ฅ๐ฅ, ๐ฅโฅ0@&๐ฅ(โ๐ฅ), ๐ฅ<0)โค y ={โ(๐ฅ^2, ๐ฅโฅ0@&โ๐ฅ^2, ๐ฅ<0)โค Area Required = Area ABO + Area DCO Area ABO Area ABO =โซ_(โ1)^0โใ๐ฆ ๐๐ฅใ Here, ๐ฆ=ใโ๐ฅใ^2 Therefore, Area ABO =โซ_(โ1)^0โใใโ๐ฅใ^2 ๐๐ฅใ ใ=โ[๐ฅ^3/3]ใ_(โ1)^0 =โ[0^3/3โ(โ1)^3/3] =(โ1)/3 Since Area is always positive, Area ABO = 1/3 Area DCO Area DCO =โซ_0^1โใ๐ฆ ๐๐ฅใ Here, ๐ฆ=๐ฅ^2 Therefore, Area DCO =โซ_0^1โใ๐ฅ^2 ๐๐ฅใ ใ=[๐ฅ^3/3]ใ_0^1 =1/3 [1^3โ0^3 ] =1/3 [1โ0] =1/3 โด Required Area = Area ABO + Area DCO =1/3+1/3 =2/3 So, Option C is Correct
Miscellaneous
Misc 1 (ii) Important
Misc 2 Deleted for CBSE Board 2022 Exams
Misc 3
Misc 4 Important
Misc 5 Important
Misc 6 Important Deleted for CBSE Board 2022 Exams
Misc 7 Deleted for CBSE Board 2022 Exams
Misc 8 Deleted for CBSE Board 2022 Exams
Misc 9 Important Deleted for CBSE Board 2022 Exams
Misc 10 Deleted for CBSE Board 2022 Exams
Misc 11 Important
Misc 12 Important Deleted for CBSE Board 2022 Exams
Misc 13
Misc 14 Important
Misc 15 Deleted for CBSE Board 2022 Exams
Misc 16 (MCQ)
Misc 17 (MCQ) Important You are here
Misc 18 (MCQ) Deleted for CBSE Board 2022 Exams
Misc 19 (MCQ) Important Deleted for CBSE Board 2022 Exams
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