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Misc 16 - Area bounded by y = x3, the x-axis, x = -2, 1 - Miscellaneou

Misc 16 - Chapter 8 Class 12 Application of Integrals - Part 2
Misc 16 - Chapter 8 Class 12 Application of Integrals - Part 3


Transcript

Misc 16 Area bounded by the curve 𝑦=π‘₯3, the π‘₯-axis and the ordinates π‘₯ = – 2 and π‘₯ = 1 is (A) – 9 (B) (βˆ’15)/4 (C) 15/4 (D) 17/4 Area Required = Area ABO + Area DCO Area ABO Area ABO =∫_(βˆ’2)^0▒〖𝑦 𝑑π‘₯γ€— Here, 𝑦=π‘₯^3 Therefore, Area ABO =∫_(βˆ’2)^0β–’γ€–π‘₯^3 𝑑π‘₯γ€— γ€–=[π‘₯^4/4]γ€—_(βˆ’2)^0 =1/4 [0βˆ’(βˆ’2)^4 ] =1/4 Γ— (βˆ’16) =βˆ’4 Since Area is always positive, Area ABO = 4 Area DCO Area DCO = ∫_0^1▒〖𝑦 𝑑π‘₯γ€— =∫_0^1β–’γ€–π‘₯^3 𝑑π‘₯γ€— =[π‘₯^4/4]_0^1 =1/4 [1^3βˆ’0^3 ] =1/4 ∴ Area Required = Area ABO + Area DCO =4+1/4 =17/4 ∴ D is the Correct Option

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.