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Last updated at Dec. 12, 2019 by Teachoo

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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

Misc 2 Not in Syllabus - CBSE Exams 2021

Misc 3

Misc 4 Important

Misc 5 Important

Misc 6 Important

Misc 7

Misc 8

Misc 9 Important

Misc 10

Misc 11 Important

Misc 12 Important Not in Syllabus - CBSE Exams 2021

Misc 13

Misc 14 Important

Misc 15 Not in Syllabus - CBSE Exams 2021

Misc 16

Misc 17 Important You are here

Misc 18 Not in Syllabus - CBSE Exams 2021

Misc 19 Important Not in Syllabus - CBSE Exams 2021

About the Author

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.